@TruckOSaurus and Spedfrom, when will be the our first civ4 online match? I'm waiting for you people to contact me :P

Wow! That's a lot of choice! I'll be glued to my computer forever! Thanks!

First and foremost get steam and Left 4 Dead, after that pre order Diablo 3 and Starcraft 2.

Then some other good choices, Fallout 3, Oblivion, and Mass Effect.

Errr... let's see. 8 yrs... well, some of these are gonna be multiplat, and I'll mention some older titles you may have overlooked:

I've *'d FPS' which you may want to try before you buy.

The Witcher
Crysis*
Orange Box* (Portal is definately worth buying alone if you don't like the rest)
Age of Empires III (Complete edition now available I believe)
Rise of Nations
Any "Total War" game
Left 4 Dead*
Counterstrike: Source*
Far Cry* (1)
Neverwinter Nights 2 & expansions (1st one is better if you haven't played it)
Oblivion
Fallout 3
Darwinia
Civilisation IV
Spore
Mass Effect
Day of Defeat: Source*
Risen (just released, PC version meant to be quite good)
Bioshock*
Unreal Tournament 2004 & 3
Dragon Age: Origins (soon to be released)
Mount and Blade
Trine

Older:
Deus Ex & sequel (sequel is nowhere near as good mind)
Planescape Torment
Baldurs Gate 2
Fallout 1&2
Age of Mythology
Age of Empires I & II
Warcraft III + expansion
Rise and Fall: Civilisations at War

Also, most multiplats tend to look better on a half-decent PC so a game like Modern Warfare 2 is usually a good bet on PC. In general, Steam is a good place to browse for hidden gems that you may have missed, and they do lots of good deals. Steam is essential for my PC gaming thesedays.

Probably a few days after I receive my new laptop.

Portal
Europa Universalis III
Sins of a Solar Empire
World of Goo
Plants vs Zombies
Audiosurf

Viva Pinata
Portal
Age of Empires 3
World of Goo(Which is cheap now I think)
Sins of a Solar Empire
Tropico 3(its not out yet, but it is looking good)
Minesweeper
Demigod

Mass Effect

Edit: How Could I forget Mass Effect?

Every game made by Valve is better on PC (and yes, they have splitscreen and wireless controllers) so Half Life 2 (+ the episodes), Team Fortress 2, Portal and Left4Dead are PC worthy, you can get them at retail or Steam...

Bethesda games also follow this rule: The Elder Scrolls IV: Oblivion & Fallout 3

Also others like

Mass effect
Bioshock
Unreal Tournament 3
The Last Remnant (if you have a PC powerful enough you won't get the 360 issues or the possible future PS3 issues)
-----------------------------------------------------
Now, only on PCs:

The Witcher
Crysis
Age of Empires III
Spore
Civ IV
Sins of a Solar Empire
The Sims 3

I second this, there're huge mods databases on the net that can greatly extend the life of these games, especially in the case of Bethesda games. I've doubled the amount of time spent on both Oblivion and Fallout 3 and Oblivion doesn't look dated anymore due to new graphics mods with newer textures.

When you get Civilization IV, make sure to download and try the mod Fall From Heaven 2, greatest mod of any game ever!
Also, may I suggest Mount & Blade? That kept me going for 14 straight hours when I got it!