First person shooters that I know have been ported to Linux include Doom/Q1/Q2/Q3. UT2003 has linux support, as does the upcomming UT2004. If you have a windows version for any of these games you can download installers to make them work in linux, since they have support from the manufactures. UT2003 I beleive has a installer for linux hidden on the cd.
Their are a few other games like The Sims which have ports to linux. Also lots of indie game manufactures support Linux, since it's easy to develop for. A good example is
garage games. They have many games that run on linux. Including the nice Orbz game, which is a cute ball game that is challeging for experianced first-person gamers, but friendly enough for most everyboy to enjoy. You just aim and shoot the ball with the mouse.

Plus it's VERY kid-friendly. Like disney-friendly, but without the satanic/evil/disney-0wNz-your-mind overtones.
The big catch is that, well, lots of Games are directX-based games. Which is windows-only and will NEVER EVER have any compatable system in Linux. MS designed it so that people who develop games for Windows using directx makes it impossible to get them to work in any other OS. Good thing is that Linux has good OpenGL support, so porting games that use OpenGL is not terrificly hard. Plus since directx is only usefull in Windows, it means that it is only usefull for creating games. Any sort of 3-d imagining/design programs will always use OpenGL compared to DirectX, simply because then you could make it run in Mac's and Unix, which are usually first choices for high-end stuff.
Other thing to look at are
winex. This provides functionality for windows-only directx games.
Any game which uses Directx your going to get a performance hit. Maybe 20-40% depending on the games. This is because of the extra layers of programming to create compatability.
However, lots of games use directx, but don't realy use it to run 3-d gaming stuff. They do that in OpenGL, but they use it in the menus and the splash screen and stuff. "Black and White" is a good example (from what I understand, but don't quote me) of this. With games like these the performance hit is smaller, like 5-15% since WineX tries to run OpenGL as natively as possible.
Halflife and BF1942 are directx games that run in linux using WineX. They both have 4 stars compatability with WineX, which means that they will probably work well, but maybe with some visual artifacts occasionally or something like that. 5 stars means that it is as good as it gets. CounterStrike mod, however has only 2 stars, which basicly means that it sometimes run well enough to pull off a couple screenshots, but that is about it. Check out the compatability lists for on the WineX site for details.
If you like that sort of game you could check out Urban Terror and Truecombat mods for Quake3. They run natively in Linux and are very challenging. Most counterstrike people get spanked for the first few times they play these mods, especially truecombat.
However, truth be known, if you use your PC only to play games, then unfortunately linux still leaves a lot to be desired.