Personally, I am a sucker for Role playing game/Adventure/Horror/First person shooter's (In one game).
So my absolute favorite is ''The Darkness'' which I had for X360, and a close runner up is ''BioShock'' which I also had for the X360. That is, before the Xbox decided to self destruct.
But I also LOVE the Legend of Zelda games for the N64. :3
Fallout 3 is pretty cool . I love the Brothers in Arms series though... I'm a big fan of first person shooters - makes you feel like you're really in the game.
Diablo 2 Lord of Destruction, I've put more hours into that game then any other and enjoyed every minute of it. The game's 10 years old, still has a large player base and just recently was patched with bug fixes/features. Diablo 3 is on the way though and in the future I hope I'll be naming it as my favorite.
Probably a game called Ultima Online,it was a rpg mmo that was out years before WoW.It just captured that fantasy vibe so well,in that you and a group of mates or more often than not strangers would group up and go dragon hunting for gold.There was no grinding or levels..though you did have to train your skills.
Chaos Gate was amazing too when it first came out,combining warhammer and computer games should be an epic win and that game was.