Halo series - Great story, first and best FPS I played back then.
Elder scrolls series (Particularly Morrowind, Oblivion and soon Skyrim /me nerdgasm) - The sheer freedom to do what you want, where you want, how you want.
Farcry series(High hopes for 3) - Again, the sheer open world environment with the style of tactics involved. Be stealthy, be loud, be precise, whatever you wanted to do.
Minecraft - The amount of creation as well as fun, adventurey stuff that goes nicely together.
GTA series - Being the criminal, fuuuun. As well as the open world feeling.
Red Dead Redemption - Again with the open world, but the story was interesting and had memorable characters.
Demon Souls(And some day Dark Souls) - Not open world, but a beautifully blended action RPG hack 'n' slash. As well as the original story behind it, very memorable, despite it could sometimes be sick and twisted.
Dead Rising series - LOADS OF ZOMBIE KILLIN'! Need I say more?
Left 4 Dead series - Memorable characters.
The list could go on, but I think I've said enough. I'm a gamer!