I recently bought a new computer and installed Debian Linux on it instead of Windows as I have very little need for Windows. Almost everything I want to do can be done with Linux so why waste my time and money on using Windows. Debian Linux is very easy to install; download a 300MB CD image, burn a CD and use that to boot the computer. Ensure you have a working internet connection for the computer and select the configuration you want. You can download a complete installation DVD if you do not have access to the internet for the new computer. I always use the testing aka etch distribution as it is a good compromise between recent versions and stability.
Debian Linux comes with a few games installed as standard; various simple arcade, board, card, kids, and strategy games. I don’t play a lot of games but I do like the simplicity and addictiveness of Tux Race aka Planet Penguin Racer, which is a 3D penguin sliding down various snow, ice and rock courses. It is available as a Debian package (planetpenguin-racer) so you can install it using apt or aptitude. Have a look at http://projects.planetpenguin.de/racer/ for more information.
If you like First Person Shooter (FPS) games then there is the open source Nexuiz available, which is similar to Quake, Doom, Wolfenstein. It makes good use of my NVidia graphics card.