The only film that made me cry (like a baby) is Hotaru no haka.
Others only made my eyes wet: The Green Mile, Crash, Das Leben der Anderen, Okuribito, Big Fish, and many more. Some short films can be just as emotional: Father and Daughter, Tsumiki no ie...
And although not a movie, Futurama has a few great episodes in this category.
Most of the time, musical scores have a great influence on all this.