i'm currently enjoying the synergy HL2 coop mod.... it works really well, and there are some custom made maps as well designed for 16 people....
otherwise, the inevitable TF2, COD4 and UT3 spring to mind.
COD2 can not be beat at online. No shooter (except for COD1) is as fun or addicting to play. Not COD4, not TF2, not UT3, absolutely nothing. For strategy games, Civ4 is amazing to play single player and even more fun online (that will definitely absorb you for hours). Another strategy game is COH. Very fun and except for the quitters, fun to play online too.
I also think that B2142 is great, BF2 is good also.
+1 for the newer BF series.
Land mark on-line games and ones I like returning to frequently. I read a lot of bad things about BF2 and BF2142. If you don't have a decent PC then you will have problems with BF2 (it needs fast HDs to avoid long map load times and 2Gb RAM). Looking forward to BF3 unless its consolized/ over-DRM'd (I won't buy a game with limited installs).
Going back to UT2004 after BF2 makes it look very dated (despite the fact it appeared so great when it first came out).
I am having a bit of a gaming old skool session with HL2 just now (single player) from the Orange Box. I just love the engine and gameplay. I hear a lot of good things about CS:S (an update of Counter Strike with the same Source engine as HL2).
I tried TF2 but it hasn't grabbed me so far... I could be in the minority there though!!
F.E.A.R. Combat: what better than playing F.E.A.R. online, and also for free! It really grabbed me, at least till I played the full single player campaign.
Quake III: this game's a classic of MP gaming. Very good gameplay, and a great sensation of adrenaline makes this very enjoyable.
Unreal Tournament 2004: I know it looks dated for modern standards, but as I haven't played UT3 yet (my PC can't handle it) it's still a great game, at least in my opinion.
Star Wars Jedi Knight Jedi Academy: Great game, and an excellent MP experience. You can throw force powers to your foes and personalise your lightsaber. Perhaps I enjoy more the prequel: Jedi Outcast.
SWAT3: Nowadays nobody plays it anymore (or at least almost no one), but back in the good ol' days it was pretty fun to hang around with 3 more ppl and try to win a mission in co-op mode (or beat them up with paint balls! xD).