Gaming in Linux is still somewhat behind Gaming in the rest of the world and if your hoping to be able to play all your games for Windows in Linux then you may have a small struggle ahead of you. However one company is helping to make things easier for Linux Gaming. Transgaming produce a program called WineX that is a more advanced version of the Windows emulator Wine that has been specially written for gaming. Though the site does require you to pay $5 a month in order to use the program, this is because certain files are copyrighted.
However you can download a free version and compile it yourself, this gives you OpenGL drivers which are an alternative to DirectX that can be used to play games just the same as Direct3D would. Transgaming currently doesn't support all games but a lot of the big titles are supported including Civ3, Diablo 2, Max Payne, GTA3 and The Sims.
I full list can be found here Some newer games you may find come with Linux installers with them, for instance I brought a copy of UT2003 a few weeks ago and found that on the third CD there was a Linux installer, I did have a few problems with mounting and dismounting drives but this wasn't too hard to get around.
Once installed the game played as well as it did in Windows, which is a massive step forward for me in Linux gaming. You can also buy a seperate Gaming pack for Mandrake Linux, this comes with games like The Sims and uses Transgamings technology in order to work. Hopefully more games will come with Linux installations in the near future.