Cocksucker Blues
For the first time in this article, a movie that wasn't banned by an oppressive government group! Cocksucker Blues was a documentary created about the 1972 Rolling Stones US tour that was just a bit too revealing for the band's comfort. They barred the movie from being released, edited portions themselves, and decided that the movie could only be shown four times a year.
The Vanishing Prairie
Disney only has a couple of movies that have been banned, and even those are tame considering the context. The Vanishing Prairie was one of the earliest household nature documentaries. However, the movie got banned because it showed footage of a buffalo giving birth, which was a bannable offense in New York in the 1950s. The ban was lifted two years after it was instated.