Probably Quake 1 is my favorite for both single player and multiplayer. It has a solid single player experience, extremely fun to play and even scary sometimes. And the multiplayer was fun too!
For story and immersion in single player: Half Life 1, AvP 2, FEAR 1 (there are others, but these are in my top list)
For fun factor: Duke Nukem 3D, Serious Sam
For multiplayer and team based gameplay: Enemy Territory and ET: Quake Wars
Since the OP said FPS and there were still people saying "Portal", I'll have to break the rules too and say "TES Morrowind" as the best single player experience ever, the best story line, the best pacing, the best immersion, the best music score and the best graphics at the time, even if it wasn't strictly a FPS.
For story and immersion in single player: Half Life 1, AvP 2, FEAR 1 (there are others, but these are in my top list)
For fun factor: Duke Nukem 3D, Serious Sam
For multiplayer and team based gameplay: Enemy Territory and ET: Quake Wars
Since the OP said FPS and there were still people saying "Portal", I'll have to break the rules too and say "TES Morrowind" as the best single player experience ever, the best story line, the best pacing, the best immersion, the best music score and the best graphics at the time, even if it wasn't strictly a FPS.