"Always Thought that I'd See You Again" by James Taylor.
"Colors of the Wind" from Pochohantas. (Has to be the one from the movie. Vanessa Williams' rendition, although nice, doesn't invoke the same emotions for me.)
"Wind Beneath My Wings" sometimes does it for me.
Sorry, I can't say "Amazing Grace" makes me cry, unless they are tears of dread. I really, really don't like that song. Never have. It's kind of like cantelope for me. I like the smell of that melon, but I can't get over the taste of it. Blech. I know I should try to like Amazing Grace, just can't get past the mecabre of it.