Al Gore's first appearance on "Futurama" aired in May of 2000, when he was still the vice president and was gearing up for his own run for the presidency, making it a beneficial arrangement for both parties. "Futurama" scored a big-name guest star, while Gore had a chance to reach out to a new audience of voters.
His continued involvement with the show, however, may have been due to an unusual family connection. Gore's daughter, Kristin Gore, worked as a writer for the show during Season 3 and 4, even receiving full credit for one of the show's best episodes, "Leela's Homeworld," per IMDb. Kristen remained involved with "Futurama" through the final season of its original run and served as a story editor for the last episode aired after the show's first cancellation, "The Devil's Hands are Idle Playthings."
The Gore family's association with "Futurama" may be the reason why the politician was willing to appear during both revivals of the show. The first, in "Bender's Big Score," was a part of Comedy Central's initiative to bring the show back with four feature-length films, which were each composed of four episode-length segments. Al Gore's next and final appearance was during Season 6 in "The Futurama Holiday Spectacular," after Comedy Central had brought the show back for its first of two revival seasons.