Not sure that there is one film that I could single out. I think most have been mentioned already, but the ones that have either moved me to tears or affected me profoundly are:
West Side Story
Brokeback Mountain
The Boy in the Striped Pyjamas
Sophie's Choice
Schindler's List
Crash (that scene with the little girl)
The Deerhunter
Breakfast at Tiffany's
I dare say there are more, but these are the ones that immediately spring to mind.