Some games I've enjoyed the last few years:

Newer PC games

Grand Theft Auto series (III and up)    Free-roaming action, great fun, both for playing and råning
Mafia                                   Like a high-quality GTA with less freedom
Railroad Tycoon II                      it's even better than the Sid Meier original
Hitman: Blood money                     High quality game, what else to say?
The typing of the dead                  Hilarious zombie horror typing game. A cult classic!
Dance Dance Revolution (Stepmania)      A brilliant form of exercise, step on arrows in time with the music
Alpha Centauri: Alien Crossfire         A great follow-up to Civilization

Console games

Katamari Damacy                         Extremely fun, strange and stylish, irresistible music
We Love Katamari                        Better in any way than the predecessor, except the music
Mercenaries: Playground of destruction  A fun war action game with lots of freedom
Guitar Hero                             More fun than playing real guitar
Burnout series                          Great "racing" game, the crash mode is great fun
Bully                                   Great Grand Theft Auto "spin-off"

Small and fun games

Bricks                                  Classic block sliding game, freeware
BD4                                     Fantastic remake of Boulderdash and Emerald mine with online
                                        high scores, freeware
Tile world                              A remake of Chip's Challenge, freeware

Classics

Civilization 2: Multiplayer Gold ed.    The best version of the best strategy game ever made
Colonization                            One of the best strategy games ever made
Maniac Mansion, ...,  Grim Fandango     The best adventure games ever made, period.

There are really too many classics that I bother to mention all of them.