Cube.
http://cubeengine.com/
The game is basically quake I/II. Might as well be anyway.
Nexuiz.
http://www.alientrap.org/nexuiz/
Currently what I am playing now. It's an online FPS, again, a lot like quake. Fast servers, not very much lag, graphics aren't Crysis, but they do.
OpenArena.
http://www.openarena.ws/
Basically the same as Nexuiz, less graphically stunning however.
Wolfenstein: Enemy Territory. (ET)
http://enemy-territory.4players.de:1041/news.php
More for the graphically inclined.
Urban Terror.
http://www.urbanterror.net/news.php
Think of it as an expansion to Enemy Territory, or not.
Americas Army.
http://www.americasarmy.com/
Nice Army sim.
Battle for Wesnoth
http://www.wesnoth.org/
This is pretty addicting, MMORPG, great gameplay.
Tremulous
http://tremulous.net/
From what I see
It looks pretty sick. I read some on the wiki, and apparently it is a fairly large, growing FPS. I haven't played this yet, but it looks interesting.
True Combat: Elite
http://www.tcelite.net/
Soldiers of Fortune clone...ish.
Assault Cube
http://assault.cubers.net/
Pretty Run N Gun.
Sauerbraten
http://sauerbraten.org/
This is my personal favorite. Good graphics, fast server, good weapons, it just all around makes a nice FOSS game.