My favorite would have to be Goldeneye. I used to eat, sleep, and breath that game with my friends. Pretty much every weekend for about 2 years after it came out we'd be up playing it. In junior high nearly the whole football team would go to my house in between when school let out and when our game was and we'd play goldeneye. Hell, I'd have people I didn't know well at all stop by and play and we'd always have fun.
Some other favorites:
Duke Nukem 64. I know its crappy compared to the PC version and it really wasn't that good, but we had a blast playing it. Co-op was pretty fun, except for a few levels in where we couldn't figure out where we were supposed to be going (was in some weird level where you're in a huge canyon or something). We'd wander around for hours before finally stumbling upon the end. The multiplayer was fun. I remember one stage with a castle and a ship where someone could get a jetpack and camp up where a rocket launcher would be and then use the heatsinking rockets to kill people all over the stage (one time I was up there and had one of my friends respanw like 5 times in a row on the ship, which made him an easy kill). Its amazing how much playing with good friends can make even crappy games fun.
Halo (original on Xbox). The co-op in it was really fun as well. Playing through on Legendary really was much better. I just really liked the environments (other than the library) and it was enjoyable. The multiplayer is decent but not that much fun, probably because I'm just so bad at it. We'd still play it for hours though, mostly just running into each other in warthogs. I had a really memorable capture the flag match, where I was stuck on a team with one of my friends who sucks beyond comprehension, and he even left halfway through the match, but I still managed to win (the last flag was crazy because I was running from the other two who both had warthogs, or maybe they were both in one).
Chronicles of Riddick. Not really a fan of the game's univers or anything, but this game is pretty awesome. Really exceptional.
Perfect Dark. Ahead of its time. Has options out the wazoo. The co-op was decent, but not exceptional. Really didn't care for the last several levels of the story. The multiplayer was crazy though. We played it a lot, and it was quite a bit of fun. Didn't quite live up to Goldeneye in fun, but I think this was because my friends only ever wanted to play against bots, and its just more fun to play against each other.
Far Cry I liked but didn't really play through it much. I'm wantjng to play Instincts.
Doom 3. I liked it, but it does get old after a while. Definitely doesn't live up to the Doom name. I would've like a bit faster pace and more enemies and ammo.
UT2K4. I really like the gameplay. I like the pace and fast action. I only like some of the weapons though. I haven't played it much, but if I had friends who played it I know I'd probably still be playing it. Wasn't into PCs for the earlier ones.