The Skills to Pay the Bills
Ok, so if you're still with me, on to how to actually land this job. What kind of skills do you need? If you're a programmer, obviously you're going to need to know how to program. Most places will expect you to know C++, though a few are still set in the ways of C. If you've got a degree in Computer Science, they won't be showing you anything you don't already know. And thanks to the crunch times, you'll probably see a lot of code that scares the heck out of you. Experience with assembly is useful, but only if you want that to be your area of expertise. Assembly is usually reserved only for rendering, since that's the bottleneck on most platforms. Assembly on pretty much any machine will do, since you can't exactly run PS2, Xbox, and GameCube code on your own.
3D math is helpful in a few areas, mainly physics and rendering. If you don't want that to be your area of expertise, it's not really necessary.
If you don't have a CS degree, get yourself some books on C++, download a free compiler, and get learning.
Having a specialty is always helpful; it can get you niche jobs that are hard to fill. For example, if you know how to write plugins for Maya, lots of places need that.
For artists, there isn't a whole lot I can tell you. If you're a traditional artist, you'll obviously need to know Photoshop, and if you're a modeler, most places I know of use Maya.
For QA, you need to play lots of games. Lots of games. And you need to know how to break them. If you try hard enough, you can break just about any game - walking through walls and the like. Oh, and you should like doing that, too. :-)