Well, I don't know about the saddest movie, but when the Zefferelli version of
Romeo and Juliet came out (oh, about 1968 or so), the first time I saw it in the theater, I started crying at the first line and didn't stop until the thing was over. So, I didn't actually see it very well...but I went back twice that week to see it again. Fortunately, those times, the waterworks didn't start quite so soon. As to why it is sad...if you don't know in regards to this one, I'm not telling.
I am another one, like Book Stop and Nesacat, who cry during lots of movies, tv shows (I don't think there was ever an episode of
The West Wing that didn't get me going at some point or other), while reading books, listening to music, and so forth. But it also depends on my mood. Still, there are some movies that make me cry every single.
The example that comes to mind first is
A League of Their Own. Yeah, I know, not really the saddest film in the world. But every time it gets to the part where the girl who was raised by her father leaves home, I just lose it. See, I'm tearing up just writing about it here. Then again, at the end of the film, when they have the reunion at the Baseball Hall of Fame, it starts all over again.