Lots of my favourites have been mentioned, and showing how little I play FPS's now a lot of them are the older games mentioned.
Half Life (I've only ever played the first game, but I am confident that it stands up to the sequals)
Deus Ex (one of my favourite games ever)
Doom 2 (probably the single game I have played through the most)
Goldeneye (still the definitive multiplayer FPS experience for me, though Timesplitters 2 was close)
I could also throw the Metroid Prime games in, but I don't really feel like they are true FPS games.