The most traumatic I can think of was probably Interstellar; I'll put why under spoilers just in case.
Grave Of The Fireflies made me want to curl up in a ball for days.
The Fall made me sob and laugh and sob.
And bloody Big Hero 6 took me completely by surprise and I blubbed all over that too.
I think the film that's made me cry for the most amount of time.. YEARS is The Never Ending Story. I watched it a lot as a child, it was one of my favourites, but that damn horse. Every time Artax died, BECAUSE HE GAVE UP, I ugly cried.