As everyone knows, Wolfenstein invented the FPS (although I'd love to find any primitive predecessors to it. I have difficulty imagining that the concept didn't exist until then). Doom is what established FPS popularity.
Obviously Half-Life on to Bioshock gave FPSs a real single player experience while Quake/Unreal/Halo made it multiplayer. MW2 has the tightest controls (though I haven't played everything that's out there). But really, the play remains the same with variations on speed, cover or lack thereof, game modes, etc.
Oh, and Killzone2 made it 'realistic' by never killing the thing you're shooting at.
My lament, though, is that while FPSs find different ways to stay fun, they don't do so by deepening the strategy. Granted, different weapons open up room for different techniques (eg. Halo's Assault Rifle/melee/grenade lethality), but essentially, you're still running on reflexes and instinct with a few different moves for each game. You can certainly pull off some awesome kills or make a crazy random kill, but there's little room for creativity or innovation, I think.
I say this as someone quite good at FPSs, but I do hope the godlike or their fans understand that in terms of competition, a 3rd person game controlling multiple pieces just provides more depth than playing single player. This translates the same if we compare fencing to chess. The first person is driven more by instinct/tactics and the 3rd by control/strategy. Ultimately, there's nothing wrong about the 1st person. It just has its own limits, as do everything else. I only bring this up to say that while I'm sure future FPSs will find new ways to be awesome, they won't be able to offer much more than what Wolfenstein already has.