The original run of The Jetsons had one season. Hanna-Barbera’s first production of the series aired on ABC during the 1962–1963 television season and contained 24 episodes.
The show was created as a space-age counterpart to The Flintstones. It debuted in prime time on September 23, 1962, but weak ratings led ABC to cancel it after its first season. The network then scheduled reruns on Saturday mornings, where the series became much more popular and remained a familiar part of children’s television for years.
The biggest source of confusion is the show’s later revival. New episodes were produced for syndication in the 1980s: 41 episodes were made for the 1985 revival, followed by 10 more commonly grouped as a third season in 1987. As a result, complete-series listings count three seasons and 75 episodes, but only the first season belongs to the original 1960s run.
The original 24 episodes were later combined with the revival episodes for syndication. Therefore, “one season” is the precise answer when the question distinguishes the original run from the entire franchise.