You absolutely must play Freelancer (thanks for the reminder Ny) if you're into space shooters. Hell, even if you're not you should play it. It roxxorz teh proverbial soxxorz.
I'd also recommend Supreme Commander (preferably of the Forged Alliance variety) to anyone remotely into RTS games. It's a tad slower burning than most RTS games but there's so much variety in the strategies. I can offer a complete, 100% Aranthos-certified guarantee that it'll last a shitload longer than ANY of the CnC games if you can be arsed trying different tactics. I've been playing the CnC3 RA beta (thanks Fileplanet!) and while it's pretty, and it's definitely CnC Red Alert in gameplay style, I wonder why I was ever a fan of the series. It's just so shallow. There are approximately 1 ways to play and win in my experience.
Enough RTS rambling, now onto FPS... The whole Half Life series is awesome. Recommend you pick up the whole pack through Steam. I think it's like 90 bucks, but you get an entire series of games for it so it's a deal and a half.
I think those are the 2 most important genres covered. Also note that I only mentioned space shooter because Freelancer is quite frankly the only game in its genre I have ever liked for more than a day. It's also one of very, very few games I still play so long after having purchased it.
If you want a game that'll provide a quick giggle, look for any of the Porrasturvat games. Truck Dismout is good, though somewhat odd. One game that had me bent double with laughter (or at least as far as someone can be bent double when sitting on a chair...) was SumoTori. Seriously. Just watching those characters struggle to stay upright is ace.
Oooh, just thought of another one. Go download Soldat. I don't care what sort of games you like, just go and download it. It's sort of a big crazy mashup of Quake, Counterstrike and 2D, and I promise you'll like it even if you don't like those three things (I did!). Forget everything you knew about sidescrolling platforming online shooters and just play it.
Sorry I dragged on a bit there, I kept thinking of new games to add to the list as I typed.
Oh, got another one. Trackmania. Aranthos says go get Nations Forever (free

), and if you like it buy United Forever. Custom car skins, a track builder, time of day lighting, replay editors, custom car models, it's a master of all trades. For some idea of what's possible with it, watch this:
http://www.youtube.com/watch?v=zG5XJY18y-o