Honestly, any movie that has an animal dying in it, I'm probably going to choke up.
A few I can think of:
I Am Legend (He had to kill his own dog!??! Now that's depressing)
City Slickers 2...I believe. When the goat got stuck in the current of the river and was crying and crying, but kept floating down stream. That was painful.
I only legit cry when the movie allows the audience to familiarize and bond with the animal in the movie, I don't cry whenever a horse gets shot in a war movie. I do hate when that happens though. It makes me sad panda.
I don't cry in dramas, they just bore me to high heaven.
EDIT: Alright after going back and reading everyone else's, it reminded me that I did tear up at the end of Click. And HOLY HELL was that unexpected. And judging by Deja's comment below me, I would DEFINITELY cry if I saw Marley and Me, which now I will not do.