Grave of the Fireflies: Semibiographical story about two children who starve to death after the bombing of Japan in World War II.
Beauty and the Beast (1946 and 1991): Story about a prince who is changed into a beast and can only regain human form if he learns to love someone besides himself. The 1991 version is a musical and my all time favorite movie.
Puella Magi Madoka Magica parts 1 and 2: A group of middle school girls are offered a chance to have one wish granted in exchange for battling witches and about a million times better than I just made it sound.
Les Miserables (2012): Musical drama about a prisoner who breaks his parole and raises the daughter of a prostitute while trying to avoid being recaptured.
Titanic: Love story that takes place aboard the famous ship.
Nausicaa of the Valley of the Wind: Post-apocalyptic film about humans trying to survive alongside giant insects and a poisonous jungle that is consuming the earth.
The Passion of Joan of Arc: Recreation of the trial of Joan of Arc who was accused of blasphemy when she claimed to see visions of the Archangel Michael.
The Lord of the Rings trilogy: Movie trilogy about the quest to save Middle Earth by destroying the One Ring. You probably already knew that though. :P
Old Yeller: Movie about a boy who raises a stray dog on a Texas ranch.