There was a Duck Dodgers animated series that run for 39 episodes from 2003 to 2005 based off the original Duck Dodgers in the 24+1/2th Century animated short from 1953.
Beavis and Butthead started out as characters in a Mike Judge short called Frog Baseball. Just one appearance before their series.
Bea Arthur appeared as Maude twice on All in the Family before the series was created.
Frasier was not a sketch on Cheers but perhaps the Carla’s ex-husband’s brief appearances on the show could be considered sketch equivalents. His character, Nick Tortelli and other family members appeared in their own forgettable series, The Tortellis. After it’s thankfully brief run the characters of Nick, his 2nd wife, his and Carla’s son Anthony, and Anthony’s wife returned to appearances on Cheers where they had played earlier.
Going back before television, The Three Stooges first appeared as part of the vaudeville act Ted Healy and His Stooges. After some movie appearances the Stooges dumped Healy for their own series of movie shorts.
Do cartoons count?
Ruth Buzzi and Atre Johnson’s park bench characters had a short Saturday morning series as “The Nitwits.”
Elvira, Mistress of the Dark and The Pee Wee Herman Show started off as Groundlings sketches. The Ed Grimley cartoon traces back to SCTV sketches.
Sasha Baron Cohen’s character of Ali G started in segments on The 11 O’Clock Show before getting his own series.
Absolutely Fabulous started out as a sketch from the French & Saunders show. Dawn French played the daughter in the sketch.
I envy you not having your brain remind you of dreck like Will Ferrell and Chris Kattan’s clubbin’ bros, and Julia Sweeney’s androgynous “Pat” character. I could go on, but this is painful…
Were either of those turned into TV shows?
Oops, sorry, those were movies.
Don’t forget The Ladies Man and Wayne’s World.
Were those turned into TV shows?
No, movies also. I don’t know why it’s restricted to TV shows, but other types of productions arising from sketches are interesting to note. At a different point in time TV series could have been the preferred outcome instead of movies.
The character of Swiss Toni first appeared on the UK comedy sketch show The Smell of Reeves and Mortimer. The character then regularly appeared on the UK comedy sketch show The Fast Show. There was then a Swiss Toni comedy series which lasted two seasons (which since it was a UK series meant a modest 16 episodes.)
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The British (6 episode) TV series Nathan Barley originated as a recurring bit on Charlie Brooker’s web site TVGoHome (which parodied TV listings).
Now that I have checked on Wiki I see another Fast Show character, Billy Bleach, managed a single season (8 episodes) series which was called Grass. Don’t recall watching it myself.
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The Steve Coogan comedy character Alan Partridge was created for radio sketch shows. Transferred over to TV sketch shows and ended up with a TV series before continuing on for a Movie and books.
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Nm—I thought the OP was asking for films.
Ehh kinda. Cassandra Peterson was usually eye candy while she was a Groundling but said she only had one recurring character which was a Valley Girl. She used that character as the base for Elvira’s personality but Elvira was original to the Horror host gig.
Yogi Bear started out as a featured segment on the Huckleberry Hound show. The bear proved more popular than the dog and he got his own, more successful show. In fact, while Yogi was around in syndication for years, Huckleberry seemed to disappear.
Elvira was a copy (but not a steal, really) of the much-earlier Vampira. The original actress, who had been offered a chance to revive her old show, bailed out and lost interest in the character until Peterson got really popular. Of course, a lawsuit followed. Peterson won.