Some movies are so sad and intense that it becomes impossible to cry--not with that stone sitting in the middle of your chest. For me such movies include Passion of the Christ, The Killing Fields, The Road, and Schindler's List.
Other movies are simply tragic but in a good way. For example, the sacrifice of the self for the greater good (Casablanca and the classic good-versus-evil movies, such as the Lord of the Rings); the sacrifice of the self for one's faith (Quo Vadis); and, any dog-loves-man-and-then-dies movie such as Marley and Me.
Finally, some movies elicit cries because of their extraordinary depiction of nobility, goodness, beauty and the human condition. I was affected by movies as diverse as Lawrence of Arabia, Babette's Spring, Manon of the Spring, As Good As It Gets, One Flew Over the Cuckoo's Nest, Cinema Paradiso, Ben Hur, Dr. Zhivago, It's A Wonderful Life, Gone with the Wind, Ghandi, Patton, 2001: A Space Odyssey, On the Waterfront, The Godfather 1 and II, Gladiator, Steel Magnolias, Terms of Endearment, many Broadway or Disney musicals, Strictly Ballroom, Amadeus, Kolya, Bridge on River Kwai, and Gold Rush.
When did I have time to do anything else?