FPS
Half Life series! It starts with Half Life 1, which was a pre-2000 game so don't expect much in terms of graphics. But it's a legendary FPS! The sequels will blow your mind away....excellent story, gameplay as well as graphics! Half Life 2; Half Life 2 Episode 1; Half Life 2 Episode 2. You 'must' give these a shot!
Then there is:
Crysis
Crysis Warhead
Metro 2033
Aliens v. Predators
Call of Duty 4: Modern Warfare
Call of Duty 5: World at War
Call of Duty 6: Modern Warfare 2
Call of Duty 7: Black Ops
BioShock 1&2
Dead Space (for horror!)
Left 4 Dead 1&2...endless hours of online multiplayer
Doom 3
Quake 4
RPG:
Deus Ex: Invisible War
Splinter Cell: Conviction
Fallout 3
Fallout: New Vegas
Try the above for a guaranteed good time!