Shooters vary in type, so I definitely count Metroid Prime (trilogy) as a FPS, with action/adventure elements. There aren't really that many "pure" FPS titles out there. Most have other elements. It's pretty much an FPS/FPA hybrid, so I definitely count is as one of my favorite FPS (Metroid Prime Trilogy version over Echoes and Corruption Trilogy versions). Goldeneye 007 is still one of my favorites. One of the most incredible games. Ever. FPS would not be what it is today without it. Perfect Dark... I enjoyed it a lot, but I never really got attached to it. I also really enjoy Call of Duty (except WaW), but I prefer Medal of Honor over CoD any day. I'm so happy a new Medal of Honor is coming out.
Others... Gears of War. I freakin' love Gears. Can't wait for Gears 3! And... omg, Jet Force Gemini was such an amazing game. Memorable in so many ways. I only wish it'd be remade or given a sequel. And, I guess you can count Resident Evil 4 and 5 shooters... honestly, I hated 4 and think the play style didn't fit it at all. Resident Evil 5, however, I really, really like as long as its co-op (otherwise, the horrible partner AI is enough to make me want to snap the disc in half).
....shooters are probably my favorite type of game. It's hard to name a number one favorite of all of them... I guesss.... mmm...nnn...aaaugh, I don't know! Ikaruga, maybe? That game is.. insane.