My favorite FPS ever is Call of Duty: Black Ops.
The campaign was awesome with lots of great moments and missions like the escape from a Gulag, the destruction of the Soyuz 2 and especially the parts set in Vietnam. The best part about the campaign in my eyes was the inclusion of real historical figures such as JFK and Castro into a fictional story.
The multiplayer in Black Ops is much slower and more tactical than those in later entries. The highest killstreak in the game is 11, which is pretty low compared to the other games in the series after MW2. Overall, it's my favorite multiplayer of any game ever.
But the best part about Black Ops, and the reason it's my favorite FPS ever, is the Zombies mode. I must've spent around 200 hours playing "Kino der Toten", and at least the same amount of time on all the other maps combined. Instead of sleeping, many nights were spent slaying zombies with friends, strangers or by myself. In my opinion, zombies mode has never reached the quality of Black Ops ever again.
To sum up, Call of Duty: Black Ops has in my opinion the best multiplayer of all time, one of the greatest FPS campaigns ever as well as the most addicting and engaging zombies/horde mode ever created. It's by far my favorite FPS game and definitely in my Top 10 games of all time.