In my opinion, one of the most touching stories ever in a game is the story of "Richard and Alice"

I didn't play it myself but I watched a let's player named Cryaotic play and it's real damn emotional and unique. Can't think of other ways to describe the game.
I even think it would be cool if the game was made into a movie.

You can watch Cry play it here
Cry Plays: Richard and Alice playlist

If you're the kind of person who loves feely stuff, you won't regret watching it. I'm not that kind of person and I think the shit was great.