Well, the games I play quite often are,
F.E.A.R. (Single player is awesome) and multiplayer can be real fun
Splinter Cell - Double Agent, really cool. The online multiplayer took some getting used to, as I´m used to using the P90 ripp off that uses a tazer
thing instead of bullets. (Sorry, I don´t know how to describe it.) But got real fun once I got the hang of using the hacking thing.
Quake II - Both single player and multiplayer is great fun
Rainbow Six - Vegas is pretty cool, I haven´t gamed it that much, but I´ve enjoyed the little I have gamed
PREY is quite fun, it´s got a cool single player campaign, and the multiplayer is fun and fast.
D00M III is aging, but I still find it to make me jump. Online is meh, but you can get a coop mode that makes it really fun, LastManStanding mode is
Battle Field 2 is really good, 2142 is enjoyable, but I prefer BF2. (The kills are more rewarding IMO.)
Day of Defeat Source. I really like that game. I play as the Germans and mount a MG42 and rank up on kills til a sniper takes me out. lol Also
playing as a regular assualt is quite rewarding too.
I really enjoy Counter Strike Source. I played 1.6 for a while (non source) and got good, but I couldn´t say no to updated graphics! (So shoot me
Halo is pretty fun, and Halo 2 should be out in a little while. Multiplayer on those are really fun. (Except when you meet those "1337" noobs that
yell "h4h4, 1 p4wn3d j00 n00b!" that just gets annoying.)
Also, Joint Operations - Typhoon Rising (and it´s expanstion packs) pack a lot of fun. I haven´t played it for about six months, so I´m not sure
what the online status of them are. But you get custom "coop" maps that are pretty fun, especially when you get a group of people that work in a
team, but I think Battlefield 2 pretty much took over.
Tom Clany´s Ghost Recon - Advanced Warfighter is pretty cool. Not sure how the multiplayer part is though.
Those are the ones (not already listed before my post) that I enjoy, but I recommend you to try out Shadows of Chernobyl. And before you play, do a
google search for "Pripyat" and "Chernobyl" so you can see exactly where you are supposed to be playing, and hopefully learn a little from the
real horrors that happened to the people and the place. (Sorry for being a downer, but I´ve gamed with a few people who didn´t know about it. And
I just felt that it´s a good thing to know that it actually happened, that people suffered, and are still suffering because the government didn´t
act fast enough.)
Hope the list gave you some ideas.