I am strange--I get moved by lots of movies and get wrapped up in storytelling all the time, but it's extremely rare for me to cry. I don't think I cried in any of the common "tearjerker" movies! And I tend to actively seek out sad movies, so it's all a bit odd.
The movie Fluke still makes me a little teary sometimes, though. I've seen in a thousand times, but the scene with the tombstone at the end just gets me for some reason. I don't think I properly cried, but I know I got teary at the end of Pan's Labyrinth.
The documentary Earthlings made me cry harder than any piece of media has made me cry, ever, but that's all real footage, so...
To be honest, what makes me cry more often than live action movies for some reason is anime. Maybe it's because they're longer and give me more time to get attached to the characters. Sometimes they trigger me just right and off I go. I bawled at a few particular scenes at the end of Dennou Coil, started crying at the end of Last Exile (I'm not even sure why on that one), cried after the credits rolled on Cowboy Bebop, got rather teary during Grave of the Fireflies, and I sometimes tear up in the ends of Wolf's Rain and Millennium Actress. I think an episode each of Natsume Yuujinchou and Mushishi got me seeing blurry, too.
There were a few Pokémon episodes and movies that made me tear up, as silly as that may seem to those who did not grow up with Pokémon.