Actually physically getting humans and their life support to Mars is likely to be feasible. But there is much more to it than that. 

LANDING SAFELY

First - they have to land there safely. Landing on Mars is far harder than anywhere else in the inner solar system, if you need a soft landing. 

The problem is - that the atmosphere is so thin, it's not enough to slow you down to a soft landing even with huge parachutes. But it is still enough so that as soon as you hit the Mars atmosphere you are totally committed.

This Hubble photograph of Mars shows the two polar caps, and clouds over the Hellas impact crater. - more Hubble photographs of Mars.
In the case of the lunar landings, right up to the last minute, the astronauts could choose to abort and fly back to orbit.
Apollo 11 landing Side by side view of Apollo 11's descent - narrated by Neil Armstrong, 
 Shows the view out of the lunar module's window side by side with the broader panorama from google Moon, reconstructed from recent Lunar Reconnaissance Orbiter data.  Original side by side Video created by GoneToPlaid - news story about his video.

The Apollo astronauts encountered several glitches during the landing, and finally landed with only seconds of fuel left. See also What went wrong on the Apollo 11 moon landing

The Apollo crew could have aborted at any stage during this landing sequence and simply flown back into orbit again.

In case of Mars, that's not feasible because you've lost so much energy through atmospheric friction.

Escaping from Mars back to orbit again is only something you would do after you get there - with present day technology anyway - most likely using fuel you created on the surface of Mars from feedstock transported there earlier in a previous mission.


Mars Direct - The Mars Society

Mars direct idea to create fuel on the surface from hydrogen feedstock for the return journey - unlike Apollo you have to land on the surface first and refuel before you have a chance to escape back to orbit, 

So you are committed to the atmosphere, but to an atmosphere that isn't capable of giving you a soft landing. It's no surprise that we have had so many hard landings on Mars.

It's not for nothing that they called the Curiosity landing "seven minutes of terror".

Seven Minutes of Terror: The Challenges of Getting to Mars

If they are lucky, first few spacecraft might land there safely. But that doesn't mean it is safe. Might just be luck. For instance many space shuttles flew safely before each of the two disasters. 


Columbia taking off on its final mission. The many successful missions before were no guarantee of success; it crashed on re-entry to Earth due to the foam blocks issue.

Designing a human rated spacecraft to land safely on Mars is probably of similar order of complexity to designing the space shuttle.

LIFE SUPPORT

We have no experience at all of long term life support in space in a closed system. With the ISS they depend on sending tons of material to the habitat every few months - and disposing of tons of material also. They can't even wash their own clothes but just burn them up in the atmosphere and get clean clothes sent up to them again.

Progress (spacecraft) - there are three or four flights per year, just to supply materials to the ISS. The spacecraft is then kept attached to the ISS, and filled with waste materials which burn up in the atmosphere when it is discarded.

You can't have progress spacecraft continually supplying essential materials to interplanetary spacecraft in this way - and we have not yet tested a spacecraft able to maintain a crew in space for a year or more without continual resupply from Earth

To go straight from the ISS to an interplanetary flight, even a first fly by as in the Inspiration Mars plans or the double Athena, is a huge leap, I don't think we are ready for that yet. First wet need to demonstrate in practice that whatever idea you have for long term life support is reliable, and can work for years on end. And test it  properly with humans on board for the duration of the test mission, and test it in space, not on the Earth.

If we could do this on the ISS it would hugely reduce the costs of supporting the astronauts in space. If astronauts could be healthy for years on end in space also, you'd only need a mission to the ISS every year or two. That we haven't managed to do that yet shows how difficult the task is.

I think the issues of long term life support are greatly underestimated by the optimists. It may be that there are simple ways to do it, e.g. algae for oxygen or whatever. But this needs to be demonstrated first.

RADIATION

Colonists on Mars would be troglodytes. It's okay to live there for a year or two probably, if you don't mind an extra risk of 3% of cancer that would on average cut your life short by 15 years if you get it. But anyone living there long term would be limited to a couple of hours a day in the open in a spacesuit. That's also your limit, not just for spacesuits, but also, on travel in vehicles over the surface, and your time in greenhouses exposed to natural light, because the small amount of air in a greenhouse wouldn't provide much protection from the hugely penetrating cosmic radiation.

This shows cosmic radiation damage of DNA. On the surface of Mars every cell will get hit many times by highly energetic cosmic rays, which on Earth are absorbed by our thick atmosphere and the magnetosphere. Mars has no thick atmosphere and almost no magnetic field.

Most colonists would spend as much time indoors as possible. If you limit yourself to a couple of hours out of doors (including in vehicles) a day, that leaves you with a 3% extra risk of a cancer, as best as we can estimate it at present. Of those who die from cancer, on average their life expectancy will be reduced by 15 years (these figures have large error margins).

It's like living on Earth immediately after a global nuclear war, worse probably, to try to live on Mars with the cosmic radiation.

Most of your life you'd need to be protected by meters of regolith from the cosmic radiation.

Fetus's and young children are especially vulnerable and young or pregnant wouldn't be permitted to go outside at all probably.

GRAVITY EFFECTS

The low gravity has unknown effects on human body. It might be that Martian gravity would stop your bones from growing and mean that you lose bone mass, just like for zero gravity. The optimists say that your body would develop normally on Mars and just have much weaker bones, whatever you need for the Martian environment. But we didn't evolve on Mars, and that's really hopeful thinking rather than good science I think. It might well be that young children for instance have no bone growth on Mars in their legs and arms and weight bearing parts of their body. It might be that it's impossible to give birth and for a fetus to grow normally in the Mars gravity.

This is simply unknown at present, we need to know the answers before anyone contemplates long term residence in low g environments.

EXPENSE OF LIVING CONDITIONS ON MARS

If you want to build on Mars you need your buildings to be able to withstand tons per square meter of outwards pressure. You need to make all your oxygen from the water or similar sources. There's no way this is going to be as easy as living on Earth, it's going to be hugely expensive - or a massive amount of your time.



Close up of the ISS, the modules have to be engineered to withstand ten tons per square meter outwards pressure, and windows especially are hard to make. You will never be able to build a normal house on Mars, in the next few centuries at least but have to build massively constructed structures like this, with few windows, just to contain the air.
 
Yes could have domes for greenhouses on Mars - but they also have to be spherical or almost spherical in structure and made of strong materials able to withstand ten tons per square meter outward pressure.. You can't just build a lightweight greenhouse like you can on Earth, so living on Mars would always be hugely more difficult than living on the Earth at least with present day technology.

And you depend on complex equipment to stay alive. Even spacesuits are pretty expensive items - and if you damage your spacesuit, probably you can't repair it, but are stranded in your habitat until someone can send you a repalcement.

The environment regulation is hugely complicated - at least until we get to the point where you can have natural Biosphere 2 type atmosphere generation - a dozen or more different poisonous gases that can build up in a human habitat, in case of the ISS system. And this is going to be more complex than the ISS because the ISS depends on ability to vent gases into space and constant supply of oxygen from Earth, and is no way a closed system.

It's really only a place that multi-billionaires could contemplate living long term - or ordinary people if massively subsidised to hundreds of millions of dollars per person.

Yes perhaps as Elon Musk proposes, you could physically get people to Mars, land them there, for your $500,000, but could you keep them alive, and would they be alive when they get there, and how much would it cost long term to support them?

PROBLEMS WITH THE BASIC MOTIVATION

The biggest problem though is with the motivation behind it, that you go to Mars for a second home or to escape from Earth. There is no way that Mars is gong to be a second home in that sense. And terraforming is a thousand year long project even for the most optimistic, Chris McKay, in one of his papers, estimates that it would take 100,000 years for photosynthesis to fix enough carbon from the atmosphere.

That means - that you are doing it, not to solve problems in our present generation, but because you think our descendants 1000 years from now will appreciate what you are doing. But - they might not, what we do to Mars now might cause problems 1000 years from now if we do things that mess Mars up through carelessness.

CONTAMINATING MARS

This is the biggy for me. There is no way we can send humans to Mars without greatly increasing the risk of introducing Earth life to the planet. 

The easiest way to see that is, that if you have a hard landing on Mars, then the crashed spacecraft would be an immediate huge fail of our efforts under COSPAR to keep Mars clear of Earth life contamination. 

Mars Polar lander - as it should have been, artist's impression. Sadly, it crashed during the landing, probably because of a program design error - the software didn't take account of vibrations caused when the legs deployed, although this was a known issue, and interpreted this as landing, and so cut off the engine too soon.

It is a potential contamination risk for Mars. Hopefully some time as our technology matures, we can go back and recover the debris and either sterilize it or remove it from the Mars surface

If humans crash on Mars similarly, it's a huge immediate fail of planetary protection. With dead bodies on the surface, together with their food, water, air, then there would be hundreds of trillions of microbes in tens of thousands of species - most unknown to science as only a tiny percentage of microbes have ever been characterized and studied - and the Martian dust storms could spread this to anywhere on the surface of Mars, and there are many microbes that we know can enter highly resistant dormant states - and that can also survive in Mars analog habitats and grow there, for some of the habitats we are almost certain exist on Mars.

I'd say that the same also applies for humans on the surface, it's not feasible to land a biohazard containment laboratory on Mars with Earth microbes in the habitats as the biohazard to contain, and spacesuits leak air constantly through the joints. And the habitats can't possibly be totally closed system, will be various wastes that get vented, and if any humans die, their bodies won't be recycled in such small habitats, or kept permanently inside the habitats, I'm pretty sure.

But the most obvious thing is the hard landing. There is simply no way around that on modern technology as far as I can see, human crash on Mars is an immediate fail. Which is especially important now, that we realize there probably are habitats on Mars for present day life, not just past life.

That includes the warm seasonal flows discovered to exist even in equatorial regions last year - almost certainly flowing water or salty water, no alternative plausible explanation been published for them - surprising though that is. They form on sun facing slopes, in the spring through to autumn, get longer as it gets warmer, far too warm for dry ice, and wrong season for wind effects and no correlation with wind. Not been totally proved yet but it's almost impossible to imagine any other explanation working.

Locations of Warm Seasonal Flows shown with black stars, some of them in the equatorial regions of Mars. These are believed to be signs of water flowing, due to the temperature range at which they form and location (not to be confused with the dry gulleys, which are a CO2 phenomenon). This is one of the most promising habitats for life on Mars, though there are other possibilities as well. See Water seems to flow freely on Mars (Nature article).

Then the DLR experiments showing that lichens and cyanobacteria can survive and metabolize in the Mars like environment using just the night time humidity of the air, even when exposed to the UV in partially shaded locations.

Then also the deliquescing salts possible habitat discovered by Phoenix - again not proved, but seems very likely, that in some places right mixtures of salts, that you get thin layers a few mms thick of liquid below the surface of the soil, that in some cases, life could inhabit. Plus solid state greenhouse effect could melt ice near the Martian geysers (though probably dry ice phenomenon, still could be melted ice there as well).

So, there is plenty to contaminate. And the global dust storms able to take hardy spores imbedded in a grain of dust anywhere on Mars, protected also from UV by the iron oxides in the dust.

Much of this is new research in just the last few years, especially the equatorial warm seasonal flows and the DLR results.

INESTIMABLE KNOWLEDGE WE MIGHT GAIN FROM MARS

Then there's also the growing realization of how much we could learn from Mars. We know so little about the early stages of evolution. According to one estimate there have been as many major steps of evolution between amino acids and the most primitive living cells we know as there have been between them and us - and we know nothing about how that happened and what those steps were.

Here is a video animation of transcription and translation all the way from DNA through RNA to Haemoglobin (in this example), 

This shows how complex even the simplest cells we know are - this is just one stage of one of themany processes going on in every single living cell -a million chemicals in a complex dance. They couldn't have arisen by chance directly from amino acids. We have no idea how a primitive cell evolved from the basic amino acids.


This diagram shows the complexity of the DNA as measured using the number of functional non redundant nucleotides. 

This is  a better measure of the genetic complexity of the organism than the total length of its DNA. Some microbes have more DNA than a human being - much of that used for other purposes rather than for genetic coding, the so called C Value Enigma. Measuring it this way deals with that issue.

Notice that the prokaryotes are well over half way between the amino acids and ourselves.

And Mars had an ocean early on and could tell us much about this because unlike Earth, without continental drift, it almost certainly has deposits from those times, that are in pristine condition pretty much. But not near the surface now, because of cosmic radiation, at least the best deposits, probably a few meters down say 10 meters below surface and hard to find, though some may be more recently exposed again. 

Same also for present day life, the habitats are rare and hard to study, unless there is life almost everywhere on Mars as in the DLR idea - if so we might find it early on - but if not -then it might take decades.

So - we need to give ourselves time to search for this properly.

And the instruments we use are sensitive to just a single amino acid in a gram of soil, say, or able to detect a single DNA molecule. They'd be hugely confused by contamination by Earth life.

Raman spectrometer able to do highly sensitive non destructive analysis able to detect molecular structure -one of the Exomars instruments
 
 
Field testing of the Exomars Raman spectrometer

These instruments are so sensitive they'd be hugely confused by any contamination of Mars by Earth life and give ambiguous results.

And - Robert Zubrin argued that we'd easily be able to separate out Earth life contamination from Mars life but that's not true. 

First of all, of course you'd not be able to detect life on Mars any more by simple detection of chirality or biosignatures because that wouldn't distinguish Mars from Earth life, so would set back our understanding of Mars tremendously, make it vastly more complex.

Then, especially for the archaea, then many entire phyla of archaea are simply unknown. This is the problem of microbial dark matter

We know they exist, through indirect evidence, but haven''t e.g. DNA sequenced them and can't cultivate them and don't know anything about them, how they live, what they do etc. And most microbes have not been DNA sequenced even of the well studied ones.

see How Many Microbes Are Hiding Among Us?, and Bringing Microbial Dark Matter Into the Light

WHAT WE CAN DO INSTEAD

Well - we don't need to give up on the whole idea. It's landing humans on the surface that's the big issue.

But - we can have humans living in orbit around Mars - no problem so long as really careful. E..g. wouldn't use aerobraking. 

But you can get into a highly elliptical Mars capture orbit - very useful for colonies and for studying the planet - for less delta v than the surface of the Moon. It's a sun precessing Molniya orbit, comes in close over the surface of Mars twice a day, on sunny side, on opposite sides of Mars. A spectacular orbit to live in with Mars continually changing size in the sky and a close fly-by twice a day.


See:  HERRO mission to mars using telerobotic surface exploration from orbit

And  gives control of robots on the surface with near real time tele-presence on opposite sides of Mars every day. With that, you could drive e.g. Curiosity at tens of kilometers per hour over the surface. Rapidly explore large areas of Mars.

I'd do it using all the same technology as for Mars surface  - making fuel for your vehicles on the surface from the atmosphere + hydrogen feed stock - and thin film solar panels for lots of power for low amounts of weight lifted from Earth - all that stuff - but with the astronauts operating them from orbit.

And use the ideas for human habitas in orbit. Safer anyway - humans don't need to do the dangerous descent to Mars - and it's just the rovers on the surface that do that. And they can explore areas on Mars that would be far too dangerous for a human in a spacesuit. And - admittedly telepresence so far is not quite as agile and mobile as humans on the surface - but neither are spacesuits - and not clear at all that spacesuits do better than telerobots.

Even a few years back, the HERRO mission study came up with the conclusion that humans in orbit doing science by telepresence could do as much science as three similar missions on the surface, for a lower cost, less danger to humans - and of course - much reduced risk of contaminating Mars.

The 2013 Telerobotics Symposium explored ways of studying Mars by telerobotics.

NEED FOR PRECURSOR MISSION E.G. TO L2 FAR SIDE OF MOON

But I don't think it's safe to do an interplanetary mission at all right now. We should do a precursor mission to far side of the Moon. And not just a few days fly by. Instead - send astronauts to the L2 position for several years - WITH NO RESUPPLY FROM THE EARTH - and see if they can last out. If not, then we shouldn't do interplanetary missions until we sort out the problems making it unsafe for humans to spend several years at a time in L2. 

And if it works, then it means we could have continual human presence at L2 for far lower cost than the ISS - it's all the supply missions to he ISS and need to change the crew every few months that make it so expensive to maintain.

The Moon also is of immense interest to study - to scientists at least. Those who don't find the Moon interesting because it's "already been done" would find Mars just as uninteresting a few years after it has "been done".

After a several years long precursoor to L2 - and lots for them to do - exploring far side of Moon + poles via telepresence - and building long wave radio telescopes on the far side - and searching for traces of meteorites from early Earth on the lunar surface and exploring caves and geology of the Moon - and testing the telerobotics needed to make all that possible - it would be a really interesting mission for the astronauts involved. 

It's like this NASA concept NASA Eyes Plan for Deep-Space Outpost Near the Moon


This shows how astronauts would control rovers on the surface of the Moon by telerobotics

Robotic roll-out of an antenna — part of a low-frequency array of radio antennas to observe the first stars in the early universe.

While doing this, they'd also be testing artificial gravity + whatever else they use to mitigate the effects of cosmic radiation. Would be a really interesting mission for those who are interested in such things, and those who aren't - I think would in practice soon get totally bored by a mission to Mars anyway. It would be a bit like a mission to Antarctica - interesting to start with - but if you haven't got a lot of scientific interest or some other reason to be there - then you'd soon get tired of the cold, and the long nights.

So after several years of that, once we are sure we can reliably send a spacecraft away from Earth for years at a time safely - then could send humans to Mars orbit. 

But not right away. I think thats' unwise and unsafe. And to the surface - even more so - that's making an irreversible decision to contaminate Mars - and the colonists simply don't have legal or moral right to do that for the rest of us.

COLLECTIVE SENSE ORGANS FOR HUMANKIND ON MARS

This idea that perhaps we shouldn't send humans to the surface of Mars because we'd contaminate it with Earth life is not much mentioned in the news. Out of dozens of news stories about ideas for human missions to Mars, perhaps only one or two will ever even mention it as an issue.

But it's frequently mentioned in the academic literature on spaceflight, with many publications debating the issue, and several planetary protection workshops on human missions to Mars. It's just that their deliberations rarely get into the news.

Here is a quote from "When Bioshperes Collide":

"One of the most reliable ways to reduce the risk of forward contamination during visits to extraterrestrial bodies is to make those visits only with robotic spacecraft. Sending a person to Mars would be, for some observers, more exciting. But in the view of much of the space science community, robotic missions are the way to accomplish the maximum amount of scientific inquiry since valuable fuel and shipboard power do not have to be expended in transporting and operating the equipment to keep a human crew alive and healthy. And very important to planetary protection goals, robotic craft can be thoroughly sterilized, while humans cannot. Such a difference can be critical in protecting sensitive targets, such as the special regions of Mars, from forward contamination.

Perhaps a change in the public's perspective as to just what today's robotic missions really are would be helpful in deciding what types of missions are important to implement. In the opinion of Terence Johnson, who has played a major role in many of NASA's robotic missions, including serving as the project scientist for the Galileo mission and the planned Europa Orbiter mission, the term "robotic exploration" misses the point. NASA is actually conducting human exploration on these projects.  The mission crews that sit in the control panel at JPL, "as well as everyone else who can log on to the Internet" can observe in near real-time what is going on. The spacecraft instruments, in other words, are becoming more like collective sense organs for humankind. Thus, according to Johnson, when NASA conducts it's so-called robotic missions, people all around the world are really "all standing on the bridge of Starship Enterprise". The question must thus be asked, when, if ever, is it necessary for the good of humankind to send people rather than increasingly sophisticated robots to explore other worlds"
See When Biospheres Collide

WANT TO EXPLORE THIS FURTHER?

Much more about all this on my Science20 column, see Robert Walker's blog

First of all, a common argument for going to colonize Mars is to find a second home for humanity. But, if you look at it carefully, there is no way that Mars is going to be a good place to shelter from any likely catastrophe, in the next few centuries anyway even with most optimistic ideas for terraforming.

Then,if you did survive, then after any even remotely likely disaster, the most habitable place in the solar system, the easiest place to restore and terraform after the disaster, would still be the Earth. So the best thing you could do is get back to Earth as quickly as you can. So no great benefit, just a nuisance, to be on Mars so far from the best place in the solar system to be to help with recovery of humanity.

More about that in this article: No Escape From Problems in Space Colonies - Earth is  Des Res - Even After Nuclear War or Asteroid Impact

Many more articles covering different aspects of these various questions, including:

The article you are reading right now is my answer to a question on Quora - and thought I'd put it here as well. Of course, I've covered most of this already in my other posts here, but this I think gave a slightly different interestng slant on it all.

For other answers, and so other points of view on it, see the original Quora question

How feasible is Elon Musk's idea to establish a colony on Mars in the 2020s?