Actually, not even on Windows XP you can play "all" games. I've a couple over here pretty much useless which run either with an unofficial patch or under emulation. Examples are Blair Witch, Heavy Metal FAKK2, Turok 2 and a few others.
Running games in Linux can be tricky, not even worthy sometimes. If you are a real gamer who wants to play all new releases all the time, then just forget it. Keep a dual boot with XP and Linux. Most of us do that only to play games.
But giving an straight answer: Yes, it's possible to play games in Linux. The most common way is to use an emulator as Cedega, AKA as WineX:
http://www.transgaming.com/
it ain't free, but costs like 15 bucks only, which is a symbolic price, really. I've to say that I'm quite happy with Cedega and, thanks to it, I've to boot much less into Windows eXPensive to play games. Check out their compatibility list before purchasing and see if your game is supported

. There's also a free version available through CVS, but then you've to compile it yourself and it not always work.
Some peoples use wine:
www.winehq.com
to run games as well. Here:
http://frankscorner.org/
you'll find some tutorials teaching you how to run a few games/applications through wine. I'd still use Cedega/WineX if I was you.
If you are into DOS games, check out DosBox:
http://dosbox.sourceforge.net/
it has a great compatibility list, but it's quite slow in older systems. It has even been ported over to the Xbox. It's a pretty sweet program

.
A few games come/has a Linux installer also. I remember UT2k3 having a Linux installer on the third disk. You can also find some installers here:
http://icculus.org/~ravage/
Some are pretty interesting. Unreal installer, for example, lets your run Unreal under Unreal Tournament(classic) as a mod. Pretty neat.
Also, before going into the hassle of everything I said, make sure you have your graphics card well setup with official 3D drivers. Hopefully you have a Nvidia card. I've heard ATI drivers aren't good or at least not as easy to install as Nvidia's. I can't confirm this, but my next card will surely be an ATI...
At the end, I'd say keep a dual boot. It makes your PC more versatile and if your ruin one OS, you can still use the other one for fixing. And consider a console too... since I got my Xbox, I could not be happier: No more hassle, no more tweaks, no more CS-cheaters
Good luck!