Yeah, I don't really cry but I would say Julia by the Beatles is a great one, someone said that on the first page.
Right now though, this song really does it for me, just hits me hard.
It's called Darling Be My Guest. By a band called Sovus Radio from Atlanta.
www.myspace.com/sovusradio
I urge you to hear this song, immediately. Listen to the whole thing. The first half will just put you in stasis, the middle will pick you up and move you, only to lead you to the very end, which brings you down farther then you started, and it's all very well organized and touching in my opinion.