Man....I have to go with the Halo series. I've played Halo 1, 2, 3 & Reach more than just about any other FPS out there. I didn't play a lot of Halo 4 because the campaign was kinda dull and the multiplayer got boring quickly. I went back to playing Reach multiplayer and that was probably my favorite. Now that I've won an Xbox One, I'm going to give Halo 5 a try.
With that being said, there are a ton of FPS games & series that I love. It started with Wolfenstein 3D for me, then Doom. Bioshock, Killzone, Call of Duty, Medal of Honor....I could go on & on about all the great FPS I have played.