Not many major, mainstream games run natively on GNU/Linux, but there are still plenty of gaming options - at least for the casual gamer.

Some major proprietary titles are actually released for GNU/Linux, e.g. Quake IV, Doom III, Neverwinter Nights. Also some free of charge multiplayer games such as America's Army and Return to Castle Wofenstein: Enemy Territory run on GNU/Linux.

Linux Game Publishing buy titles and port them to GNU/Linux, see:
http://www.linuxgamepublishing.com

Lots and lots more of free and non-free games exist - some small and simple, others quite big, and many very good. Check out some of these sites:
http://happypenguin.org/
http://www.tuxgames.com/
http://www.lgdb.org/
http://www.linuxgamingworld.com/

Some software available for GNU/Linux allows you to run games developed for MS Windows on GNU/Linux - ease of use and success rate may vary - however, the more popular the game, the more likely it is to be supported.

Wine (Wine Is Not an Emulator) is the first option, it's free software installable via the package manager. See the Wine app database for information on running individual games:
http://appdb.winehq.org/appbrowse.php?iCatId=2

Wine is a command line application, the syntax is:
A second option is CrossOver Games which is an effort based on Wine. See:
http://www.codeweavers.com/products/cxgames/

Another option that lets you run MS Windows games is Cedega. They have some MS Windows games officially certified for being ran this way. See:
http://www.cedega.com/

Numerous emulators exist, making it possible to run many old classic games of other platforms on GNU/Linux. For example:

• Amiga (UAE)
• Arcade (MAME)
• Atari (Stella, Steem)
• Commodore 64/128 (VICE)
• MS DOS (DOSBox, DOSEMU)
• Nintendo (infones, bsnes, nestopia)
• Play Station (pcsx, pcsx2)