Here are some of my favorite games available on Linux:
LGeneral A WWII turn-based strategy game.
Head over Heels
Navigate two characters, each with unique abilities, through a richly colored world.
Sauerbraten
(A.K.A. Cube 2) First person shooter, with online, cooperative map-editing capabilities.
Heroes'
Nibbles, only with nice effects and several alternative modes of play.
BoboBot
An unfinished platform game that hasn't been updated in a few years, but still is quite enjoyable. ASCII-based level creation.
MirrorMagic II
A challenging puzzle game involving a magic beam that is channelled through rotatable mirrors. Map editer included.
Tux Racer
Take ski-free, make it 3D, throw in a penguin, and this is what you get! Exciting, supplimentary levels can be found On-line. Create your own levels using
The GIMP.
Orbz (Commercial)
Shoot orbz around 3D maps, collecting as many stars as you can, before your opponents get them.
ThinkTanks (Commercial)
Tank game with a fun premise.
Scorched 3D
Scorced Earth redone in 3D.