When people think computer games, rarely does Linux come into the picture. This doesn't necessarily have to be the case. Linux as a wealth of "casual" games. Both KDE and GNOME have collections of games like FreeCell, Minesweeper, Bejeweled, etc.
There are also a number of quite good OpenSource and Commercial games in a variety of genres. Good sites to go to are:
On the otherhand you may already have a collection of Windows Games. Certainly this is the most likely type of computer game you will find in stores.
My basic advice to a Linux user who wants to play mainstream Windows games is to maintain a secure, well groomed "Wintendo" partition in which to play these games. This is certainly the easiest and most reliable way to get your mainstream gaming fix. It is what I do.
However, if you don't have a legitimate license of Windows or don't want to use Windows you can still play games. On a console. Go buy a PS2, XBOX or Gamecube. Seriously.
Ok so you want to play games on your PC and not use Windows. Well then, you're in for some grief. It can be done. But it isn't perfect by any stretch of the imagination. Don't believe the hype as they say.
The only really viable way to play Windows games on Linux is with Transgaming's Cedega product (what was once known as WineX). You can also use the stock WINE Windows non-emulator. But you will probably have less joy than with Cedega. Be aware that Cedega is a commercial app. It was forked off of WINE when WINE was BSD licensed. WINE is now LGPL so people can no longer do this.
Personally it has been a while since I used Cedega. I no longer subscribe to the $60USD/year 'service' so I can't test new versions. The games that I did get to run when I had a subscription were:
As you can see I didn't exactly test it with a very broad range of games. Quite a few of the games I wanted to play just plain didn't install, let alone run.
Now the marketing on the Transgaming website would have you believe that many games will run flawlessly. And they are not entirely wrong. Each version of Wine/Cedega did get better and better and "support" more titles. But the games I ran were never "perfect" or flawless. There was always some 'tweaking' to be done. Some were very good, like Diablo 2 and Warcraft 3, but they still had non-fatal but annoying glitches or reduced performance. Some Cedega users report complete "Windows like" success when running games like Half-Life 2 and Counter-Strike. The product has received many good reviews. But be aware that your mileage may vary.
Other caveats are that Cedega only really supports nVidia graphics cards for 3D games. Forget about using DRI/Mesa 3D drivers. ATI binary driver support is also patchy.