I find the story of most FF games to be good.
I'm on the fence about Final Fantasy. I think they're good, but they can feel contrived and forced. Then again, Atlas Shrugged is considered "literary" even though it's really, really terribly written, so I'll go ahead and include it.
I can't believe I forgot about these two, but Shadow of the Colossus and Ico. Actually, pretty much anything by the guys that now make up Team Ico can qualify.
Definitely. It's funny: the project lead for Ico was asked whether he considered video games an art form, and he replied "No." XD
If horror counts, the Penumbra games and Amnesia (particularly Amnesia). Not necessarily because of story, but because all of those games know exactly how to screw with the player's mind. Penumbra: Requiem in particular is basically one giant mind-screw that takes you through Philip's subconcious.
I haven't played these, yet. They're supposed to be good, though. You've reminded me of others: Silent Hill/2.
People are going to give you more examples of what they consider "Literature", than what you think it is, and this does seem to be more of a list for you, rather than a general opinion thread of what people consider games with good Literature.
Topic amended to include people who just want to list games with stories they like. Good enough?

Still got a better plot than Atlas Shrugged
Then again, the stories I wrote when I was 9 had a better plot than Atlas Shrugged...
I hate Atlas Shrugged, honestly, but it's considered a classic, so it is.
Whatever, I hear the Persona games are supposed to have good writing. But I havent played them, so cant comment.
They're okay but they get mired in too much irrelevant side stuff. Most Japanese games have this problem: they have good ideas or foundations but fail to build on them toward something meaningful.
Psychonauts?
Even though it has this kid-game vibe, it explores a multitude of minds, some orderly, some bat-[censored]-insane, and is full of little details and references to make you think. It's hard to describe with how unique it is.
I've never played this! Wasn't this a console exclusive? I think I wanted to get my hands on it, and then found out it was console-only. What a shame.