I'm always sad when Fear and Loathing finishes because I don't want the madness to end. Same with The Big Lebowski.
The scene in Highlander where his wife dies and Queen doing what they do best of course.
The Magdalene Sisters, very depressing and the fact that it was based on true events made it worse. I just cried when I saw it.
Also cried watching The Wizard of Oz... to this day I don't know why
A.I
Titanic
Moulin Rouge
Atonement
The Notebook
My Sister's Keeper
Stepmom
Million Dollar Baby
Bambi
Schindler's List
Romeo & Juliet
Requiem for a Dream (now that is just depressing to watch)
Cold Mountain
I don't really go for typical weepfests, but I find myself very tearful during the first 15 minutes of Up. Mystic River is a pretty downbeat film (naturally, given its subject matter) and had me choking back tears for most of it.