Movies are all around the Disney ships as a matter of fact. In your stateroom there are a number of movie channels playing Disney favorites all the time. Up on deck 11 there is Funnelvision which plays family friendly Disney movies all day long in front of the pool. Your little sailors can swim in the pool while watching their favorite Disney movies!
If you'd prefer to watch movies on the big screen in an air-conditioned theater then you are in luck. There is a theater that shows the first run movies pretty much all day long. When my family sailed in September of 2011 Cars 2, The Help and Fright Night were playing, just to name a few. Generally the films shown during the day are family friendly with G and PG ratings while the movies shown later in the evening might be PG-13 or R.
There is certainly a movie for everyone aboard your Disney cruise!