Apparently inspired largely by Akira Toriyama's popular Dr. Slump, Robby the Rascal is the story of Robby (Robotchi), a fun-loving, mischievous robot with a TV set in his stomach. Robby lives in a peaceful village with various other robots, all created by the eccentric and lecherous Dr. Art Deco, who has a major crush on local policewoman Sgt. Sally (Sachiko). Although he is an android and (usually inadvertently) causes much mischief, Robby has a warm, kind heart and is always willing to help out a friend in need. With his human girlfriend Tiffany (Kurumi Yukino), he gets into a variety of wacky adventures.
However, a rich, spoiled inventor named Horace (Highbrow) will stop at nothing to get Robby for his own. Much of the plot of the English feature-length dub of the anime involves Horace's attempts to threaten the peace in Robby's village, with the help of his female assistants, Tracy and Yvette. For example, in one story arc, Horace uses an illusion-causing ray gun to spoil Robby and Tiffany's spring picnic and then manages to capture the little robot and force him to compete in a high-stakes game of tennis. In another, he follows Robby, Dr. Deco and their friends to Europe, where he and Robby square off in a medieval-style joust. And in the final story arc, Horace and his minions compete against Robby and Tiffany in a global race in which the first prize is $10 million, which Dr. Deco hopes to use to start an amusement park.