For anime, I have a few picks. Topping my list is this one-shot anime short story;
Hotori - Tada Saiwai wo Koinegau
Other picks are:
Elfen Lied, of course.
Soukyuu No Fafner is filled with sadness from one end to the other, but with a good and hope-filled story.
Shingetsutan Tsukihime explored sadness fairly often
Chrno Crusade, while mostly comedy, has an ending that left me sniffling for all I was worth.
A new series that seems to have some dark human emotions in it, is
Shigofumi
If you don't mind adult anime, there's
Kite, which is sad, depressing, and unfulfilling in the end.