What kind of games do you like to play?
RPG: Baldurs Gate II enchanced edition
Pillars of Eternety
fallout 1 & 2
FPS:
while you can get most of them going back to doom by looking around - if you want multiplayer at all I suggest sticking to one made in the last 2 years - pick your flavor and go have fun
Strategy:
Civ V
(Civ IV and III are good also - the newest one is still kind of bland honestly)
Total War series
ARPG:
Diablo III
Path of Exile (ftp)
Torchwood I and II
marvel Heroes
MORPG:
World of warcraft
Everquest I and II
Guild Wars 2
RIFT
Neverwinter
Dungeons and Dragons Online
Lord of the Rings Online
give them all a try - they all have a 'try without spending a dime' mode
Action:
Tomb Raider (if you haven't played it yet - the new one is great)
Simulation:
Car Mechanic 2 (honestly it's disturbingly addictive)
Strategy 4x (you many not know this as it's not a console genre)
Sins of a Solar Empire
Starcraft 2
Warcraft III
Adventure:
Deponia the complete series
Kings Quest I - VII
Heroes Quest I-III
etc.
Great games from the past that you may or may not have an easy time tracking down (and frankly in some cases have a hard time running well on modern hardware without taking time to emulate older machines):
Freespace2
SSI Gold box RPGs
Ultima I-VII
Tex Murphy series
Gabriel Knight series
Planescape : Torment
Wing Commander series
Diablo 1 and 2
Finally - almost any game that has it a console in the past 8 years can be found on PC - that being said you can peruse 'game of the year' awards and such for gems.
http://www.pcgamer.com/the-pc-gamer-top-100/
This should have a few that interest you in that list as well