These are all free/opensource or GPL and most of them have linux clients, which is way to friggen cool. Feel free to add to the list.

FPS:
Tremulous
Nexuiz
Warsow
Legends
America’s Army
Wolfenstein: Enemy Territory
Savage: The Battle For Newerth

RTS:
TASpring - Remember Total Annihilation? :)
Warzone2100
Widelands
Glest
Battle for Wesnoth

RPG:
Sloth
PlaneShift - (MMO)
Stendhal
ManaWorld (MMO)