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The banning of films for political reasons is as old as film itself. There is no country in the world that is innocent of trying it at some time. The motive behind banning films is the fear of a regime change. No regime seems totally immune from this fear.
Sometimes the pressure to ban films comes from political groups that are not part of the regime (yet). Sometimes it comes from religious groups. But unless the regime backs the banning, often times the publicity garnered just makes the film more popular.
An example of this is 1915's Birth of a Nation, which was the target of the fledgling NAACP, first for banning, then for censorship, all of which only seemed to make it more popular. Indeed it took Gone With the Wind to eclipse its box-office numbers.
1925's Ben-Hur was banned in China in 1930 for containing "propaganda of superstitious beliefs, namely Christianity." Since Christianity itself hadn't made much of a dent on China, the ban was effective.
1940's The Great Dictator, in which Charlie Chaplin lampooned Adolf Hitler (in the role of Adenoid Hynkel) was banned in Hitler's Germany. Strangely, even Americans seemed to think that Chaplin had become too self-indulging, and this film turned out to be his last with the "little tramp" character.
More effective than banning a film is censoring it. Many governments have regular censorship bureaucracies. Depending on the country, the excuse for not letting people choose what they view is immorality/indecency, offense given to "sacred cow" groups, and threats to the regime.
The usual steps require going to court and winning. This can be expensive and time-consuming, which is just what the banners of the film want. Famous examples of banned films
Banning versus censoring
Types of films banned in most/all countries
Famous Laws used to ban/censor films
Famous organizations promoting banning/censorship of films
Mechanisms for getting films unbanned