CoD 4 and WaW were what really got me started on fps, and before that I used to love Medal of Honor Rising Sun. So those 3 I think. And the original Bad Company was awesome too!
For me it has to be either Cod4 or Bad Company 2 or Halo 3.
Certainly within my school year cod4 was the game that made online gaming popular. The single player story was amazing and the online was brilliant.
Bad Company 2, was the first Battlefield game I played, found it amazing that you could fly helicopters, drive tanks, blow walls up, gravity actually counted for something when sniping. I actually preferred this game to BF3.
Best ever, I'd have to agree with the above and say quake and/or doom. Fantastic games! However I would rank metro up there with the best, it got me back into FPS games after a long hiatus.
Medal of Honour Allied Assault for me. I spent ages playing that game, was the first PC game I played so, I might be a little rose tinted.
On console, I would have to say Halo 2 back on the original Xbox. I played in a Xbox community/non serious clan and, spent many late nights at weekend playing drunk on Halo games. Good times.