Mine has to be Halo 1, the original Halo for Xbox. Goldeneye 007 for the N64 and Unreal Tournament for the PC are also up there. I heard Half Life and Crysis for the PC are great, but I've never played those two games.
Re: Best first person shooters you've ever played?
Quake 3 Arena
Chasm: The Rift
Unreal Tournament 3
No One Lives Forever
Duke Nukem 3d
The Chronicles of Riddick: Escape from Butcher's Bay
Soldier of Fortune