Never fear, the cephalopodiatrist is here to answer this pressing concern!
Your typical squid is robust and active, packed with dense, heavy muscles. Not to mention the hard parts that are also heavier than water: the chitinous pen and braincase, and the calcified beak. This would all seem to be positive evidence for sinking squid.
But squid have two options for offsetting this weight. The first is to add material that's lighter than water. The obvious choice is air, or some other gas. Many heavier-than-water fish take this approach, in the form of swim bladders. These organs have nothing to do with voiding nitrogenous waste; rather, they contain varying amounts of gas that allow fish to "enjoy a sense of near weightlessness."
Well, that sounds pleasant! But no squid is known to store gas in a similar manner. Isn't that curious? I don't really know why, but it does save the squid from a major downside of the swim bladder: its rapid expansion when a fish is dragged to the surface by a fishing line or net. Exploding swim bladders have never posed a threat to humans (except in whimsical poetry), but they are not so healthful for the fish (although some rockfish, amazingly, are able to survive the experience).
Squid opt for non-gaseous lightweight materials, such as ammonia. Different squid have at least two different strategies for incorporating this redolent chemical into their bodies. Cranchiids, or glass squid, such as the pretty little specimen pictured below, fill a spacious cavity with ammonium chloride.
Cranchiid squid juvenile from plankton - photo Uwe Kils en:GFDL.
Architeuthis, the giant squid, incorporates individual ammonium ions throughout its body tissues instead. That's probably why giant squid are reputed not to taste very good.
Some squid--notably the Humboldt Dosidicus gigas--don't use much ammonia, but do have extremely fatty livers. Fat is buoyant (a physical truth which can be observed at any reasonably well-populated beach), so this may well be an adaptation to counteract sinking (and an excuse for a terribly punny title). But as far as I know, no one has proven it.
Okay, enough with the yucky stuff--gas and ammonia and fat. The squid's second solution to gravity is simply to put those dense muscles to work! Birds are heavier than air, but they can still fly by expending energy. Similarly, squid can expend energy to stay level or swim up. They just need to keep eating to fuel the workout.
These two teuthic strategies have been recognized for decades; in the words of squid savant Malcolm Clarke (1976):
Squids (teuthoids) fall into two distinct groups according to their density in sea water. Squids of one group are considerably denser than sea water and must swim to stop sinking; squids in the other group are nearly neutrally buoyant.The hero of Squid Drop clearly belongs to the denser-than-seawater group. But there's no need to worry that he'll be stuck at the bottom of the ocean--as long as he eats enough crabs to fuel the swim back up.
* I have not played it and I have no idea if it is awesome or lame.