The Witcher, Crysis, Call of Duty 4, Oblivion, Morrowind (Oldie but a goodie), Company of Heroes (Strategy), Supreme Commander (Strategy), Painkiller, Orange Box (Most essential game on this list), Day of Defeat: Source, Counter Strike: Source, Battlefield 2 or 2142....
If you've never played this, it's a sweet ass game and looks good to boot.
Also on the list:
HL:2 (Episode 1 and 2 as well)
COH (Company of Heroes)
How could I forget about this one?
Keep and eye out for Left 4 Dead from Valve. It's going to be a multiplayer zombie/survival game and looks promising so far.
That F.E.A.R game still scares the chit out of me. Haha.
Bioshock and F.E.A.R. are the only one's that I'll repeat, as I don't like any of the other FPSs listed.
F.E.A.R. is an amazing game, Persus Mandate even moreso. Play in surround if at all possible. And, of course, late at night, with the only light in your room being the glow from your monitor (PC and accessory LEDs are allowed too).
You're not hardcore until you finish F.E.A.R. like that. I did. Never again.