I've played Cube 2, Tremulous, and Quake 3 natively in Linux, all of which run well if you configure your graphics card properly. Other games like Jedi Academy, Quake 3 Arena (Windows version), and older games such as SimCity 2000 work well in Wine. There are also NES, SNES, N64, Genesis, etc. emulators for Linux as well as basic games (minesweeper, solitaire, tetris, etc) preinstalled on most Linux distros. I also tried Flight Gears, a free flight simulator, but it didn't like my gamepad and I kept crashing.
The GTKRadiant level editor for Quake 3 engine games also has a native Linux port that runs...in my opinion...better than the Windows one, mainly because the Windows one crashes on my laptop at 1600x1200 but the Linux one works fine.