I'm not sure if a tear has actually dropped but it has almost happened in the notebook, blue valentine, hachi a dog's tale. Fault in our stars, still alice, you're not you, one day, message in a bottle, the lost valentine, awakenings...
And I'm sure I forgot some others along the way... but you get the point
This go backs to a question @MissNowhere asked about being sad at films and we agreed that when animals got hurt or died, we were so upset. For some reason when it happened to people it didn't affect me as much. That said I must have been about 21 before I was able to watch a movie where an animal got hurt without having to turn it off because I was so upset.
I cried during the death scene of Selena, cried during Braveheart when he buries his dad and brother, and got teary eyed during the child killing scene in American Sniper (proper hate seeing/hearing children dying in movies).
Yes, for several, and for different reasons. Sense and Sensibility at the end because i was so happy they got married. Titanic because Jack died. Anytime someone is mean to an animal--I ought to have that bumber sticker that reads "I don't care who dies in the movie as long as the dog lives."
I'm not a movie crier (I'm not big on crying in general), however there have been many movies that have nearly brought me to tears. The only movie I've ever cried for was probably passion of the christ