I play FPS and RTS, so here's some games:
FPS:
Descent (gee, I reccomend this one every time right? Here's the deal. If you ever wanted to have a REALLY intresting deathmatch (or soccer match, or capture the flag, or entropy, or...), this is the game series you were looking for:
Descent I - Old pokey. Older than DoomII. On the cover of the 8th PC Gamer magazine. But it still gets along, and the D1X mods really make for some fun gameplay, if you don't mind the graphics.
Descent II - Now we're talkin. 800x600 resolution baby! Woohoo! Erhem....anyway it's got more mature multiplay code, although it's still IPX. The camplaign is good too. Oh, and did I mention the OpenGL patch and the 1000+ levels created for this game, as well as the extensive editing tools and the Napster-like level downloader Detlef?
Descent 3: What you want. Modern graphics engine (with really good fog effects), full Windows (and Linux) native, EAX audio. But sadly it's showing it's age a bit. Oh well, the SP is pretty good (kept me occupied for a loing time), and there is the best Descent multiplay yet (TCP/IP support and oline matchmaking via Gamespy and PXO. Join the fun.
Return to Castle Wolfenstien- Need I say more? Just get it!
Unreal UT2003- Ditto
Heavy Metal FAKK 2- Just for all the perver---I mean enthusiasts out there. Yeah...Ermm....anywho, it's got guns, swords, big bosses, and big...errm...let's just say Lara Croft be *deleted*
Dues Ex- If you like RPGs and First Person Shooters, you'll love this gem. Great, open action (choose stealth, hacking, or gun toting badmofo)
System Shock 2 - Like Deus Ex, but older, and a hell of alot scarrier! In fact, it's hands down the scarriest game ever!
Dakantania- Welll...ummm...err....It's hard

Yeah...on second thought...
RTS:
Warcraft III- See UT2003
Earth 2150:The Moon Project - 2 years old but a great game. Playing the SP now. It's a 3D RTS like Warcraft 3 but set in the future, with tanks, mech, and antigrav ships. And really, really big guns!
TBS:
Worms Series (especially Worms Armageddon and Worms World Party)- Excellent games with ALOT of humor and great gameplay. It's Turn based, but who cares?
Steel Panthers, World at War- Best of all, it's fricking
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-edit- Clarification on Dakantania(sp---whatever)
It's bad for your heart. And the poor soul you'll shoot after playing this game since you'll become quite suicidal and won't care about human life afterwords. Because you'll lose all faith in humanity and the gaming biz.