Before 1970: Lonely are the Brave (1962). Gah! I love love love this movie -- until the last five minutes. Then I hate it, because my heart aches and breaks, and I'm sad for days afterwards. But Kirk Douglas, that absolutely gorgeous horse, Whiskey, and one of my all-time favorite Jerry Goldsmith scores make this movie awesome despite the fact that the ending kills me even when I know it's coming.
Post 1970: Er... I can't seem to think of one. I can think of plenty of movies with sad moments, but none of them leave me feeling sad afterwards. They ultimately end happy. I can think of several downright depressing movies, but that's not the same as sad. I'm sure I'm overlooking one, but after thinking on this for a few days, I still can't come up with one. Hm.