The Brain from Planet Arous is a 1957 science-fiction film that features the theme of alien possession

Demonic possession

Demonic possession is held by many belief systems to be the control of an individual by a malevolent supernatural being. Descriptions of demonic possessions often include erased memories or personalities, convulsions, “fits” and fainting as if one were dying...

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An outer-space terrorist from a planet named Arous - a brain-shaped creature named Gor - arrives on Earth and possesses young scientist Steve March. Gor then proceeds to use his vast, destructive powers to bend the world to his will, threatening to wipe out the capital city of any nation that defies him.

Meanwhile, another brain from Arous - named Vol - arrives on Earth and eventually inhabits the body of March's fiancee's dog.