I would have to say that The Lord of the Rings is my favorite movie with spiritual themes. The depth to the story seems endless as I always find something new when I watch it. I think people are surprised when they find out how many things are applicable to spirituality in general and Christianity, and yet, the story is good enough on it's own that people can watch it and get the meaning of the story without being beaten over the head with it. Definitely LOTR for me.
I'm surprised no one mentioned Bladerunner, as the spiritual themes in that movie are rather deeply ingrained, and a bigt disturbing. There are multiple versions out however, and I'm honestly not sure I've seen them all. I've seen the theatrical, and the 80's director's cut, but I think there is a newer director's cut that I have yet to see....but it's definitely worth a look, and makes someone question what it means to be "human".
I would add Dune to my list but I don't really feel like either version (80's Lynch, early 2000's SciFi) of the movie does the book justice, but both movies have good points. I think the SciFi version gets more into the spirituality of the story, but nothing like the novel touches on. But there is a new Dune film going to be made with people from both previous versions involved, so maybe we'll get a definitive version that goes into the essence of the story more.