Have we really stopped evolving? In Cosmos magazine, Steve Jones argues that human evolution is coming to an end:
The question I have is: will human evolution really continue? I think the evidence shows that human evolution has largely come to a halt.
He lists three components necessary for human evolution:
First of all there's variation, which comes from mutation. Second, natural selection, which comes from inherited differences between individuals and their ability to reproduce.
Finally, evolution is greatly promoted by isolation.
Jones is right about the first two elements: you need variation and natural selection for evolution to happen. But Jones is wrong about the third element - it's not necessary for evolution.

We'll tackle all three elements, but let's start with the third. Isolation is important for speciation - the generation of two (or more) new species from one, but it is absolutely not necessary for evolution in general. One species can change dramatically over time, without splitting into isolated populations, as it adapts to changes in its environment, like new diseases, changes in climate, or even culturally-driven changes that affect survival. The human species itself has changed dramatically in the last 300,000 years, without splitting into new species: archaic Homo sapiens that lived 300,000 years ago were physiologically different from humans today, or even those that lived 80,000 years ago.

Species can undergo evolutionary change without isolation. Humans aren't as geographically isolated from each other as they once were, but that doesn't mean that human evolution has stalled.

Next element: variation. Jones argues that the pipeline of genetic variation is drying up: rates of new germ-line mutations (mutations that happen in sperm or egg cells, and are thus passed on to the next generation - the only kind of mutation that counts when it comes to evolution) are going down, because of changes in human reproductive patterns:
We see little evidence to say that human evolution is going to speed up because there are more mutations coming into the process. Nowadays, people start their families late, but stop early; changing demographics show that there are fewer older fathers today than in the past. So, if anything, the rate of mutation is going to slow down.

That claim is incredibly difficult to substantiate, and it's not obvious that it should be true: very recent (20th century) changes in child-bearing patterns may or may not be significant enough to have a serious impact on the rate of new germ-line mutations (and thus the generation of new genetic variation). There is no convincing evidence yet that such recent changes have dramatically altered the rate of appearance of new mutations on a global scale. 
Jones can speculate that these demographic changes have reduced germline mutation rates, but it's just as easy to think of other factors that could increase germline mutations - like laptops, whose heat output has probably increased the rate of germline mutations, at least among men in developed countries. In any case, whether the mutation rate has changed or not, germ-line mutation hasn't stopped - we're all born with new mutations.
Mutation rates aside, there is already a tremendous amount of genetic variation among humans for natural selection act on - and this variation isn't going to go away as the human population becomes more and more like a giant melting-pot: a large population with individuals that mate randomly with each other preserves its genetic variation. (You may remember the Hardy-Weinberg principle from your high school or college biology class).

Compared to say, rats or cockroaches, the human population is not that large and doesn't engage in totally random mating, but the point is this: we're not draining the pool of genetic variation by interracial marriage. Jones' is simply wrong when he claims this:
But now the world's populations are mixing at an extraordinary rate. In Britain, one marriage in 50 or so is between members of different ethnic groups. We are mixing into a global mass; the future is brown.
And this:
What we find is, even more today than in 1950, that our genes are mixing and averaging out. More and more people are subject to this averaging process. And for humans, this averaging means an end to evolution.

We may "average out" our skin color by all this mixing, but, as a species, we're not averaging out our genetic variation. There is no shortage of raw material left for selection to act on, and it's not going away any time soon.

On to the final Jones' final element of evolution: what about natural selection?

Certainly one of the most dramatic (and tragic) sources of natural selection, childhood disease, has been significantly reduced, especially in the developed world. And with fertility treatments, more and more people are able to have children.

But that doesn't mean the difference in the numbers of children people have (i.e., differences in reproductive fitness) is negligible. Jones claims:

Between 1880 and 2000, the huge variation in the average number of children born per couple between countries diminished. So, once again, there's no evidence that evolution has anything left to work with.
The flaw here is that natural selection doesn't need "huge variation in the average number of children born per couple" - very small differences add up to huge changes in the long run. (And I'm not sure why Jones' thinks that the differences have to be between countries or populations - evolutionary change can take place within a population.) Look around your neighborhood, and you'll see differences that are large enough for selection to act on. In the US, we don't all have 2.5 children: there are many, many adults who never have children, and some who have more than most of us could handle.

It doesn't take much - phenomena like the slight reproductive advantage of more closely related couples in Iceland is enough. (This study found that couples who are third or fourth cousins are more fertile than couples that aren't so closely related.)

So is human evolution grinding to a halt? There is not reason to think it is.