I think
Team Fortress 2 is a good choice, although SF4 and Gears 3 give it a run for its money.
It's an incredible looking game, even after all these years. Its character design are instantly recognizable and you know the class roles, it's small visual touches like the little red crosses that come out of the Medic's gun that immediately visualize to players how this mechanic works. Everything is just so clear and intuitive...it's a brilliant art direction, that not only gives the game a unique personality, but creates a more accessible game to play moment-to-moment.
I'm also a huge lover of objective-based gameplay in multiplayer shooters. CTF and KotH variants are instantly more appealing to me than Deathmatch, where I'm often just wondering around the map aimlessly looking for people to kill. I think having a certain hotspot area you need to get to or protect really keeps the action flowing because everyone is focused on that one spot. And to win in this game, you need teamwork, people who can play their chosen roles with skill, who understand the maps and its various chokepoints. Kill/Death ratio doesn't matter; if us winning this CTF game means me rushing out to the objective as a Scout and keeping it alive, then goddamnit it was worth the deaths.
The class-based system is great too, because of it's limits. So many other games, Medics also carry SMGs, or Engineers have assault rifles. By keeping your abilities more specific, it makes every role feel more unique. Medics are completely focused on healing your team and keeping them in the fight, with the right Uber/Krit charge. Scouts rocket around the map annoying everyone, grabbing objectives and picking off lone wolves. Spies avoid the typical pathways of other classes, being clandestine and sneaky and shit, going for those satisfying backstabs and fucking your equipment. If you ever get bored with one class, you can just switch to another and play the match entirely different.
And I really gotta hand it to Valve on how they've supported this over the years. 200+ updates, 30+ maps, new modes...all free! So many new weapons and gadgets and HATS! GLORIOUS WONDERFUL COLORFUL HATS!
Finally, this is completely anecdotal, but in my hundreds of hours playing TF2, the number of assholes I've ran into are completely overshadowed by the great people I've played with. Perhaps its the teamwork nature of the game, or the comedy inherent in so much of it, but there's a joyous atmosphere to much of TF2's mayhem that even when I lose, I'm having fun.
Its a beautiful, wonderful, fun video game. I take breaks from it now and again, and then I come back and fall in love all over. Top 5 game of the generation for me, I believe.