Personnally I think Halo is the only "pure" FPS (that I've actuall heard about), because it doesn't try to bring new stuff, or stuff from other games in it. You have guns. You have enemies. You shoot enemies. Simple as that.
No puzzles, no minigames (Bioshock style), no semi upgrades and RPG elements, just shooting. And if it innovates it's simply to give you more shooting options/more strategies to shoot stuff.
Of course, "pure" isn't necessarily "perfect" or "fun"...