How many seasons did this show last? Was
it cancelled, if so, why was it cancelled?

Out Of This World lasted four seasons (96 episodes). Four seasons is usually the maximum for sitcoms that air in first run syndication as opposed to a prime time network.

The show lasted four seasons (96 episodes in all). Some people think that the show ended because it wasn't getting as many viewers as other sitcoms, but I think the primary reason that they ended the show was because Evie (Maureen Flannigan) was getting too old. She was 18 when the show ended and the producers figured that once Evie had grown up, the show wouldn't have been as interesting.