Pure shooter: Half-life 2 has yet to be equaled for pure story-driven, variety of environments, adrenaline fueled, lengthy, huge scope, set-piece goodness.
Immersive Sim: Still Thief 2: The Metal Age (barely edging out T:TDP)
Open world: Far Cry 3? A blast to play even though the story was total shit. (Note: most open world games are 3rd person.)
RPG: I hate Skyrim. There, I said it.
Survival Horror: The first half of Resident Evil: Biohazard? I haven’t played much FPS horror.
I assume that since we’re talking about FP shooters, I can’t mention walking sims. My favorite first person game ever is Everybody’s Gone to the Rapture.
I also have to agree with many others that, for modern games, DOOM is pretty unequaled for pure slick shoot-demons-in-the-face fun mayhem.