I don't usually get sentimental over movies, but Watership Down definitely made me sad when I saw it as a kid, though I can't remember if it made me cry. I re-watched it as an adult and it had much the same effect (maybe that's because we used to have rabbits as pets so I sympathize with the little critters).
Another movie that really got to me was The Road. That is probably the only movie ever to have jerked a tear out of me as a grown man.. it just tugged at my heartstrings very forcefully. The themes it dealt with were all too familiar to me: in many ways the bleakness and hopelessness of the post-apocalyptic setting mirrored struggles I've had in my life, and the man losing his wife reminded me of losing my girlfriend. Also the way the father in the movie tried everything to keep his son alive in a world that wanted to see humanity extinguished felt like a rusty knife twisting in my heart, because my dad was never a warm, close and caring man. There were times when I felt like I had no father at all when I was growing up. Even though I have long since come to terms with what kind of a person he is, his utter absence in my life nowadays is mind-boggling. It's funny, you'd think your dad would make some effort to keep in touch since he lives in the same city, but I can't even remember the last time I got a phone call, never mind seeing him personally. I know he feels extreme guilt over his failures as a father, and he is doing a wonderful job redeeming himself with his 5-year old son from another mother, but I wish he wouldn't have written the rest of his kids off as lost causes and swept us under the rug. So yeah.. that is one major reason why The Road got to me the way it did.