Probably Moon. It just gets me thinking about humanity and morality.
There are probably more conventionally sad films out there, but Moon makes you think about things most people wouldn't even waste a second on, and that alone makes it a great film.
Its also got one of the most depressing atmospheres for a film ever. The moon. Alone. Without any real human contact for three years on a wasteland, billions of miles away from home. This movie will not make you cry. This movie will make you feel like shit all the way through your body.
A few runners up would be Pan's Labyrinth (favorite movie ever), The Wrestler, Toy Story 3, and, even though I'm not really a fan of the film, Requiem For A Dream (mostly for the mother's sake).
If you haven't seen any of these films, I recommend you do it now. Though probably not in one sitting, because you'll probably kill yourself afterwards.
EDIT:
Marter said:
<url=http://www.escapistmagazine.com/forums/read/326.231661>Snow Angels by far.
I cried throughout it.
Yes. This too. Pretty much, find a Sam Rockwell film, and you'll find depression in some way, shape, or form. God I love that man...