Left 4 dead hasn't been mentioned thatl be my vote, otherwise its Half life 2 and apologies for being such a valve fan boy here but 3rd on the list would probably be TF2 or Counter Strike.
Deus ex, Bioshock, Fallout 3 - All great games but if we're talking pure fps here I'm not sure they count, include in that list Stalker and the Thief series, these are RPG fps'eses. Acctully running around and shooting other people has imo been done best in games like Quake 3 and Painkiller they just didn't have the immersion and brillant subtly that more story/coop based fps' pull off.
Realism in shooters I'm not a big fan of despite sticking counter strike up there, COD has always been like playing through a war movie which is good in its own way and other more realistic shooters like ARMA just slow things down far too much. It's always more entertaining to be firing auto reload rockectlaunchers and taking explosions direct to the face while jumping around like a loon. Left 4 dead achieved the perfect balance between immersion and frenzy fps fun, its only downside... which is its major plus point as well, is that you can only get the most out of it playing coop.
in fact fuck it, half life 2 then, the father of all modern FPS. I'm a bottle and half of wine too soused to explain myself any better.
Quake 2 gets a mention as well.