I've played many games with one or more scenes which moved me. Like The Last Express, text adventure Trinity, Memento Mori (not a great game but that hospital scene was awesome), I Have No Mouth And I Must Scream, Dreamfall, The Path.
And then there's a recent one that really got to me.
Dear Esther. It is a love-it-or-hate-it thing. Hell, it's not even an adventure in the traditional sense but who cares when it touches a cord. I'll repeat what a reviewer said about another game: "It isn't much of a game but whatever it is, it's one hell of one of those".
I should go write about it in the Dear Esther thread...