I'm in a bit of a teary mode right now. It's not a movie but I was just watching Call of the Midwife, and I cried.

The first movie I can recall crying was Bambi, when his dad died.

Mostly is movies dealing with animals but lots of foreign movies too, they are so moving. Can't recall the name of a recent one, but it was about a slice of life, a sad man who lived alone, had no friends anymore all his family gone. In the end he died in his apt. Maybe not the happiest of movies but real.