I'll admit, when I first saw Titanic it made me cry. But I was 12. So nyah.

Lesse. The Green Mile
Forrest Gump
The Last Samurai (there's another story, but too personal)
The Return of the King (Miriel knows the score. Ohhh I cryyyyy)
I actually get a little misty during Kill Bill, volume 2.
Signs
That's all I can think of right now. :/