What films are based on a true story?

Usually any film labeled non-fiction in the film database could be based on a true story. Hollywood takes a lot of liberties with plot and characters though. For instance, "The World's Fastest Indian" was based on the life of Burt Munro, a real person. The film is riddled with errors to make the story more interesting. If the film is a documentary then the facts are more close to true.