Edit: I originally said TS2, I'm going with Future Perfect. I'm also swapping out Day of Defeat with Red Faction.
Timesplitters* Future Perfect
Tribes
Doom 2016
Red Faction*
Half Life 1 & 2
I've wanted to play Deus Ex and No One Lives Forever for awhile meow but haven't gotten around to it
Honorable mentions:
Quake 1-3, Unreal Tournament 2003 (there might be better ones but it's the last one I played), COD: WaW, Perfect Dark, AvP, Day of Defeat
Tribes and Timesplitters 2 are probably the most fun I've ever had playing FPS games for very different reasons. I absolutely adore both of them