One of the best parts about going to the movies is after you leave when you and your friends can talk about the story, share theories, and just expand the universe in your own head. A couple of great examples of this are people taking notice of how Pixar films all take place in the same universe. Also, the idea that 007 is just a number given to many different agents, which explains the multiple James Bond actors over the years is another famous fan movie theory.
Of course, those are just two examples. Peep the above video to get a more expansive view of some more interesting movie theories.