Unreal Tournament 2004 is the best multiplayer shooter ever made. Period. It's perfectly balanced, a ton of fun, and the system requirements are low - my old system is close to five years old, and it can run it at high resolutions with everything maxed out and still maintain a clean, consistent 60 fps. There aren't many quality servers out there these days, but it's amazingly fun at LAN parties and the bot AI's pretty decent at higher levels. I'd recommend Bombing Run - think football with guns. The bot AI for BR sucks, though, so if you're gonna do a botmatch, stick to CTF, Assault, or (Team) Deathmatch.
If you've got Half-Life 2, you probably have the Orange Box. If you don't, get it. Portal is innovative and fun, and Episode Two completely changes the way shooters are done; the voice acting is amazing, especially Merle Dandridge playing Alyx. Robert Guillaume as Eli also does a great job. Team Fortress 2 is an amazing, addictive shooter. For best results, you need a team that works as a team; playing it with a bunch of people that're doing their own thing just sucks balls.
Battlefield 2142 is also an excellent shooter, and is a great choice if you happen to prefer some more strategy in your shooters. Again, though, to get the most out of it, you need people that squad up and work together.
If you're wanting to give RPGs a shot, I'd suggest starting with Baldur's Gate (with Tales of the Sword Coast), Baldur's Gate II (with Throne of Bhaal), Fallout, Fallout 2, and especially Planescape: Torment. All of them should be relatively easy to find for probably $5 apiece (most come in collections now, though.) Torment may be hard to find; I guard my set of discs more than I'd guard pure gold. All of those games represent the pinnacle of RPG gaming for their time, and completely blow JPRGs like the Final Fantasy series out of the water.
If you've got an SNES (or an emulator for one, like ZSNES), I'd recommend the Mega Man X games (X, X2, X3.) If you've got a PSP, they're available on Mega Man Maverick Hunter X, which includes pretty much all of the MMX games, plus a bunch of extras like remixed soundtracks, and an animated movie thing.
Continuing with the SNES theme, you're committing a crime against gaming if you don't play Super Metroid, Super Mario World, and especially Super Mario World 2: Yoshi's Island.
If you're into RTSes, I'd suggest Starcraft (old but still as fun as always) and Warcraft III. I've heard Red Alert 3's also pretty good.
I'd recommend you give World of Warcraft another shot if you've got a group of friends (at least five of you all together), because it's incredibly fun with a good group of people to play with. It pretty well sucks if you don't.
Oh, yeah, survival horror games. The remade Resident Evil for the GCN is pretty good. Resident Evil 0 ain't bad. Resident Evil 4 is very fun. Silent Hill and Silent Hill 2 are good.