I've seen scant mention of "Forrest Gump"...one of the most heartbreaking, yet moving pictures I've ever had the pleasure of witnessing. Seriously, if you're a one-dimensional simpleton who saw the trailer and dismissed it as the story of a retard on a bench, you should definitely re-evaluate your perception after WATCHING the actual film.
Others that I can recollect: "Edward Scissorhands," "Happiness"(though sorrowful in a sickening rather than moving way), "Adaptation," "The Crow," "Life is Beautiful," "Y Tu Mama Tambien," and although it isn't a film, certain episodes of the anime series, "Cowboy Bebop," never fail to choke me up.