Of the games that have made me cry, there are a few.
Most Recently, Walking Dead is trying to work on me (Although I don't know if I want to buy the other three episodes, really), I want to well up, but I can't do it.
Bioshock's good ending made me shed a tear or two. It's a happy ending to me.
Earthbound with it's incredible ending theme does it to me.
King Kong: The Official Game of the Movie makes me cry, but it's only because of a deep dark psychological issue I have with defending things that I can't do in real life, the Kong Levels do me in.
Slightly less recent, but still fairly recent to me, Lost Odyssey, and the first story in the 1000 Year of Dreams did it to me. I remember crying quietly to myself, and the only things that came to me as I played was, "...That's so sad...." I promptly shut the game off and came back to it an hour later.