The Honeymooners started out as sketches on Jackie Gleason’s various variety shows. The Simpsons were short bits of animated filler for The Tracey Ullman Show. The Carol Burnett Show begat Mama’s Family. And after that, I draw a blank.
Certainly after more than 70 years of network television, there have to be more than three shows that started out as regular features, but not the main focus, on another show.
I know that several Saturday Night Live sketches were turned into movies so I figured that some must have been turned into series but the only one I could find was a recent streaming series based on MacGruber.
The Great White North recurring sketch on SCTV, with the characters Bob & Doug McKenzie, led to a spinoff animated series, Bob & Doug, in 2009 (nearly 30 years after the original sketches).
Rick Moranis (who had retired from acting) chose to not participate in the production of the spinoff, so Dave Coulier provided the voice of Bob McKenzie.
Aeon Flux would, I think, as it was originally a recurring segment on MTV’s animation anthology show, Liquid Television, before becoming a standalone series.
South Park, OTOH, was never part of an anthology/variety show, though it originally come out of a couple of standalone short films.
The characters of Kath, Kim and Sharon first featured in their current forms as a weekly segment of the Australian comedy series Big Girl’s Blouse (1994–95), having appeared in a more embryonic incarnation earlier in the decade on the sketch comedy show Fast Forward (1989–92).