Lawrence Block (mostly not sci-fi) did it with Getting Off. I think it was a mistake: the original couple of short stories worked much better as they were.
A short story Leiningen vs. the Ants was made into a radio play, and finally became the movie The Naked Jungle. This was back before Charlton Heston was a star, and his name was below Eleanor Powell in the credits. One small role was played by William Conrad, who had voiced Leiningen in the radio play.
Another SF example: the first Pern book, Dragonflight, was a fixup of two novelas, “Weyr Search” and “Dragon Rider”, plus some bridging material.
I thought he threw the full-length manuscript in the trash, and his wife rescued it and persuaded him to give it another chance.
The various iterations of “The Stand” were inspired by a short story called “Night Surf” which is about the aftermath of a plague called Captain Trips that is not quite as dramatic in its ability to demolish the human race as was the one in “The Stand”.
Ben Lerner expanded his short story “The Golden Vanity” into the novel 10:04.
also The Ugly Little Boy.
I’m not sure it’s an official reworking but Nabokov’s early novella The Enchanter has a lot in common with his much more famous Lolita.
I’m pretty sure Hugh Howey’s Silo books started as short stories.
Not a short story, but The Expanse series started as a roll playing game.
I came into this thread late, and most of the examples I would have given have already been used.
I’ll add that Fredric Brown (who also writes fantasy and science fiction, so he was familiar with the practice) also did this with his mysteries. His short story The Pickled Punks became the novel Madball, and his novel The Night of the Jabberwock started out as short stories.
The Wikipedia page for Fix-up lists a lot. Most of them are science fiction, but if you scroll to the bottom, there are a number of others.
Among those mentioned are
The Red Pony by John Steinbeck
The Big Four by Agatha Christie
The Big Sleep, Fairwell, My Lovely, and The Lady in the Lake, by Raymond Chandler.
I believe that one or some chapter(s) of Poul Anderson’s The Boat of a Million Years started as short stories.
I have no problem with “novelette,” unlike some authors I could name who find it too “cutesy.” “Novelet,” is brand new to me, so no comment (my spell checker doesn’t care for it, either).
Maybe we should use “novella,” for stories over 100 pages/xx0,000 words, “novelette,” for stories half-ish that length, and “short story,” (Now there’s a phrase that sounds too cutesy) for tales smaller than a novelette. Or say, “screw it.” 
The rule in nominations for the awards for Hugos and Nebulas (the two major science fiction awards) is that a short story is 7,499 words or less, a novelette is 7,500 to 17,499 words, a novella is 17,500 to 39,999 words, and a novel is 40,000 words or more. Is this arbitrary? Of course, it is. The problem is that they decided that the awards should be split into categories by length. Any such division has to be arbitrary. They presumably looked at the lengths of fictions that were being published and decided that this divided them closely enough into equal amounts in each category.
Canadian author W. O. Mitchell published the short story “The Owl and the Bens” in the Atlantic Magazine in April 1945. Subsequently, in 1947, he published the novel “Who has Seen the Wind”, in which the basic story of “The Owl” was incorporated as a sort of B-plot.
Nice! Ignorance fought, thanks.
[ “The end” – my short story just became a novelette. ]
Another Stephen King entry is “The Gunslinger”, which was first published as a short story, then a collection of short stories which became the first chapter in the full book. The book then kicked off the Dark Tower series, which now ties in a huge portion of his entire oeuvre.
“Musical fruit.”
The movie “Predestination” was based on the Heinlein short story, “-All,YouZombies-”
Wasn’t the Shawshank Redemption originally a short story?
Yes, but it wasn’t ever turned into a novel, which is what this thread is about.
For that matter, Foundation was published as a series of shorter stories.