Nexuiz [http://www.alientrap.org/nexuiz/], a quake-like multiplayer FPS, based on the Darkplaces engine.
Warsow [http://www.warsow.net/], a quake-like multiplayer FPS with a large focus on bunnyhopping and dashing.
Lemming Ball Z [http://www.lbz3d.com/], a fighting game based of that fucking shitty tv show Dragonball Z, only it's pretty good. fly around and shoot balls at the opponent, kick them, all that stuff.
Dungeon Crawl [http://www.dungeoncrawl.org/], a roguelike for literal children
Battle for Wesnoth [http://www.wesnoth.org/], a turn-based strategy game that's easy to play, and has a large focus on terrain and tactics.
Kobo Deluxe [http://olofson.net/kobodl/], an arcade-like space shooter wherein you destroy structures. good game.
Nethack [http://www.nethack.org/], the most well-known roguelike there is. complete, difficult, addicting.
Egoboo [http://egoboo.sourceforge.net/], a 3rd person dungeon-hack kinda thing. reminds me of zelda for some reason, without the overworld.
Mu-cade [http://www.asahi-net.or.jp/~cs8k-cyu/windows/mcd_e.html], an arcade-ish game, similar to geometry wars, you shoot enemies off the arena, and your tail gets longer.
Neverball [http://neverball.org/], a game wherein you manipulate a ball to go into a hole. apparently it's kinda like super monkey ball? I don't know.
Progress Quest [http://www.progressquest.com/]. this is not a game. it is not interactive. you stare at your monitor. it's okay. quite funny.
Sauerbraten [http://sauerbraten.org/], this is basically Cube2, a multiplayer FPS wherein you can edit the map in the game, I think, idk, never played it
Scorched 3d [http://www.scorched3d.co.uk/], scorched earth in 3d. shoot other tanks and shiz.
SuperTux [http://supertux.lethargik.org/], a linux mario clone, if you play this you will never know the loving touch of a woman~
Torus Trooper [http://www.asahi-net.or.jp/~cs8k-cyu/windows/tt_e.html], an arcade-like shooter game, set in a torus, a very good game.
Warzone 2100 [http://wz2100.net/], an RTS, design your own units (like, wheels or tracks, what kinda weapon, and so on), it's cool.
Armagetron Advanced [http://armagetronad.net/], you can play TRON! in 3d! revolutionary!!!!?
edit: oh wait you said "great". welp, might want to forget about supertux (like we all do)
