I don't watch many movies but the saddest I watched would have to be "My dog skip". I also watched a clip of a movie called "Hachi: a dogs tale" and try to avoid watching that movie to not become depressed, it's based on true events.

Eternal Sunshine of the Spotless Mind
The Green Mile
Manchester by the Sea
Everything is Illuminated

I'm sure there are more I'm not thinking of, but there's a good start for you.

Manchester is a really good movie. I really like it.

It's pretty rare that a movie or show makes me feel anything these days, but all four of these got me good and I loved them. I highly recommend all four of them to anyone who loves a good movie and who doesnt mind feeling a bit (or A LOT).

My Flesh and Blood

The Wrestler

Definitely Hachiko. That and La Bamba.

Aw shit, I knew there was some other good ones I was missing.