I've never cried but there's been COUNTLESS movies I've experienced an emotional shiver from watching (which is the closest thing). The most recent being Remember Me. Omg.
One of the earliest memories I had growing up was literally crying like a baby when I watched Naked Weapon. It was an all female assassin movie but the main character's best friend was killed. Made me cry sooo much!
A lot of animated movies A walk to remember, The Fault In Our Stars (the books made me cry as well)
Grey's Anatomy isn't a movie but I just have to mention it because I cry all the time watching it anyway I hate depressing movies now, I stopped watching them