Portal 1 & 2
Half-Life 2 and Episodes
Shadow of the Colossus
Call of Duty 4
Grand Theft Auto IV (would have been better if they hadn't made it a sandbox game, though)
Bioshock 1 (at least it was ambitious, even if it falls apart in quite a few places)
Assassin's Creed 1 & 2
Dead Space 2 (mostly found it engaging for personal reasons, though, and I can see how it might not have the same effect on everyone)
Red Dead Redemption
Iji (it's a freeware game, but a great one)
Mass Effect 1 & 2
Silent Hill 2
Fallout: New Vegas
That's just the ones I can think of and not counting all the great adventure games out there, or games that don't have a "story" in the usual sense, but still have powerful themes and a great sense of narrative all the same (Flower and Missile Command come to mind). Honestly, people don't give games enough credit in this area.
EDIT: Totally and utterly forgot about Echo Bazaar for some reason. Fallen London has to be one of the most interesting places any game has let me live in.
Half-Life 2 and Episodes
Shadow of the Colossus
Call of Duty 4
Grand Theft Auto IV (would have been better if they hadn't made it a sandbox game, though)
Bioshock 1 (at least it was ambitious, even if it falls apart in quite a few places)
Assassin's Creed 1 & 2
Dead Space 2 (mostly found it engaging for personal reasons, though, and I can see how it might not have the same effect on everyone)
Red Dead Redemption
Iji (it's a freeware game, but a great one)
Mass Effect 1 & 2
Silent Hill 2
Fallout: New Vegas
That's just the ones I can think of and not counting all the great adventure games out there, or games that don't have a "story" in the usual sense, but still have powerful themes and a great sense of narrative all the same (Flower and Missile Command come to mind). Honestly, people don't give games enough credit in this area.
EDIT: Totally and utterly forgot about Echo Bazaar for some reason. Fallen London has to be one of the most interesting places any game has let me live in.