Thriller makes me cry but I sense that's not what you were getting at.
I welled up at Up Down Man - it had a small national tour and recently got revived in Bristol. one of the few times 'not a dry eye in the house' was actually accurate.
War Horse definitely got me, ditto [spoiler] in the second half of Hamilton. And Everybody's Talking About Jamie is a lovely collective feel-good tear-jerker.
I had a really hard time getting through NEXT TO NORMAL and thought it was one of the most heartbreaking shows I've ever seen. I could feel all of the character's pain.