'The Entity' (1983)
The Plot: A single mother is tormented and raped by a supernatural force in her home.
The Claim: "Based on a True Story"
The Reality: The character played by Barbara Hershey in the film is based on Doris Bither, a Los Angeles woman who in 1974 claimed to have been beaten and sexually assaulted by unseen entities in her Culver City home. Two paranormal researchers, Kerry Gaynor and Barry Taff, subsequently conducted an investigation into Bithers' claims but, despite allegedly witnessing supernatural events, they were unable to capture any evidence of the entities on camera. Unlike Hershey's character, Bithers was an alcoholic whose home had been condemned twice by the city, and in real life there was (obviously) no large-scale home reconstruction like that featured in the film's silly third act. Otherwise, the main thrust of the film's plotline is relatively close to the story recounted by Bithers and the researchers.
The Verdict: You don't have to believe in the supernatural to recognize the similarities between the series of events dramatized in "The Entity" and the real-life case that inspired it.