Not bawled my eyes out..but tearful at:
Toy Story 3 (the finale when Andy gives away his toys, although the furnace scene affected me like nothing I've ever seen in the cinema).
Forrest Gump ("You died on a Saturday morning..")
The Shawshank Redemption (the hug on the beach)
Gladiator ("Go to them")
Also, I maintain that Marley and Me is a pretty awful movie, but the last five minutes...well, as a dog-lover, that got to me.
Watch My Dog Skip, I defy you not to be at least tearful when the dog dies at the end, masterfully done, closest I've ever came to tears at the cinema. Forrest Gump's my favourite film, Jenny's death is truly tragic after everything she and Forrest go through together.
As for animated films, I agree about the Toy Story films, When She Loved Me is so sad. And Toy Story 3's ending is a choker.