There's a Magic card named Flying Carpet. Early versions of it were destroyed if the creature targeted with its ability died; this part was removed in later versions, though the card is still generally considered fairly weak.
A nasty combo from the early days (after it got the buff above) was to use Flying Carpet on a nasty enemy, then use Winter's Blast to knock that creature into the graveyard. Useful if you needed to get a potentially powerful creature out of the way.
Mutts had the cat and dog duo ride on a carpet until it landed in another house inhabited by a guard dog (who happened to be a close friend). Subverted as the carpet only flew due to very strong winds rather than magic.
Imma Wiserd has Snape, who uses a giant dollar bill as a flying carpet because the author thought Snape was a Jew due to him using big words (i.e. non-slang words). When it is revealed that Snape is Vadermort, he still uses the giant dollar bill as his mount.
Disney's Aladdin and its many spin-offs featured a sentient, mute magic carpet as a character.
The fourth installment of Fantaghiro mentioned it when playing with the Flying Broomstick trope: When Xellesia and the Black Queen realize that the latter can't transform into anything that flies, they seek an alternate means, and reject carpets because they only work well in Arabian Nights Land.
J. K. Rowling's companion book to Harry Potter, Quidditch Through the Ages, claims that magic carpets are more popular than broomsticks among wizards in the Middle East and South Asia. Also, it mentions that it's illegal to import flying carpets into the United Kingdom. Canon never quite gets around to explaining why, but a somewhat popular fan theory has it that broomstick manufacturers retaining expensive lobbyists and dispensing the odd backhander have something to do with it.
The Swedish YA mystery stories about Ture Sventon features flying carpets (well, at least two of them) in what is otherwise a non-fantasy modern-day setting. It is the eponymous hero's main form of transporation in the first three novels.
Wonderfully used in Gabriel Garcia Marquez's Magical Realism book One Hundred Years of Solitude in which the gypsies bring magic carpets to show the villagers. Jose Arcadio Buendia and his son Aureliano Buendia are more awe struck from seeing ice.
Harry Dresden once tried to do this when he was a younger wizard. It didn't work. The next time he tries it it does work, when he's drawn into Molly's Battle in the Center of the Mind with The Corpsetaker. It only works here because when you're all thought and magic you don't have to worry about real life constraints like gravity and painful crash landings and can do pretty much whatever you want.
Magic carpets are used in two other Scooby episodes, "Hassle In The Castle" and "Scooby-Doo Meets The Addams Family."
Phineas and Ferb create one in "Magic Carpet Ride", there's even a song about it.
A Pixie and Dixie cartoon has Mr. Jinks obtaining a magic carpet that operates under the command "Chabunagunga."
A Dastardly & Muttley Wing Dings blackout has the pair encountering a man on a flying carpet that could not be controlled. When Dick asks what's wrong, the man says, "I just washed my carpet and I can't do a thing with it!"
A year earlier, a genie gives Dastardly a flying carpet on Wacky Races which he uses to race to the finish line. He fails after colliding with a cactus, the result of not paying attention because he was breaking the fourth wall.