Magic tricks are difficult. Audiences are cynical, and people want to know how to do them. However, in TV Shows, a Stage Magician can do amazing things, completely impossible in real life. They don't even have to bother with an explanation, "magicians never reveal their tricks" is an ideal handwave for forgoing any explanation.
Note that this trope is about explicitly non-magical tricks; using real magic in a magic show would not be an example.
Compare Impossible Thief which is a similar idea applied to the field of thievery instead of stage magic. Contrast Magicians Are Wizards.
Kaitou Kid (who started in Magic Kaito but later became a regular character in Detective Conan) often does this in a similar manner, overlapping with Impossible Thief. In his solo episode when first introduced, and before even becoming Kaitou Kid, he manages to use a lifelike dummy that isn't noticed until its head screws off, and a giant monster-shaped balloon operated by a crane outside his school window, all as part of a prank.
In a Biopic of Harry Houdini starring Tony Curtis there are several magic tricks which are presented with absolutely no explanation. Two that come to mind are, he and his wife-to-be Meet Cute while he's doing a street performance & he makes her name "magically" appear on his arm (which in reality needs a ringer and some rubber cement), and late one night he brings home a Saw a Woman in Half box and makes her get in so he can saw her in half right there & then.
Mostly averted in The Prestige, where the tricks's explanations are shown and discussed, and are easily attemptable by real illusionists. However, the greatest trick of the film, Angier's "The Transported Man" turns out to be done by a cloning machine built by Nikola Tesla.
In Terry Pratchett's Discworld, the Wizards of Unseen University, who can do real magic, are utterly disgruntled at the given fact that people will still pay real hard-earned money to see a stage magic act where everyone knows it's done by sleight-of-hand, mirrors and misdirection. This trope comes into play when the audiences think this is better than anything the wizards are capable of.
The Amazing Adventures of Kavalier and Clay: During a business meeting Kavalier's magician background comes up and he is asked for a demonstration. He manages to make a lit cigarette disappear and then reapper inside someone else's cigarette case. (Later in the story, when he's working as a professional magician, the boy whose Bar Mitzvah he's performing at catches him planting cards for a trick to be done during the banquet, so it's not like there is no acknowledgement of magic's need for setup.)
In House, a stage magician manages to pull off some amazing tricks, that impressed and stumped even House himself. One such trick was a simple "pick a card" trick. Then he threw the deck at a window, where a card stuck to the glass. When House took the card and told him it wasn't his card... he found his card, stuck to the other side of the glass.
The same actor played a magician in Just Shoot Me!, who managed to hide tickets inside an unpeeled banana... that a coworker brought from home... from across the room.
In How I Met Your Mother, Barney's role as am amateur magician leads to many instances of this. Notably the trick the TSA agent performs in "Magician's Code," although it may have been a simple card trick. Not to mention Barney's trick itself, which involves a broadsword (that he somehow pulled out of a 1 foot by 1 foot box... that had just been scanned by airport security).
For all the jokes about GOB's illusions on Arrested Development, Tony Wonder did manage to have himself baked into a loaf of bread and turned into a giant sandwich for the troops.
In Drake & Josh, a magician is actually able to somehow make the titular characters' father's hair disappear and stuff a girl into a large popcorn holder (without anyone even noticing).
Pushing Daisies has a few examples in the episode "Oh oh oh it's Magic." While several tricks of the episode are explained throughout the course of the episode, a couple are patently impossible (including the twins elevating a Lovely Assistant with bolts of electricity).
In The Brady Bunch episode "Lights Out", Peter takes up magic for his school talent show. He does some classic tricks like the interlocking metal rings, pouring disappearing milk, and he builds a "vanishing lady" cabinet. But one simple trick was actually impossible. He takes two empty cardboard tubes and puts one around a bottle. The bottle disappears and reappears inside the other tube. Not complicated, but not possible without TV magic.
In the episode of The X-Files "The Amazing Maleeni", the stage magician Maleeni has a magic trick where he rotates his head 360 degrees around. Every other trick performed in the episode is possible in real life.
In an episode of The Mentalist Jane entertains some local kids with a magic trick: he makes a coin disappear from his hand and appear in the pocket of a boy standing in front of him, without having had an opportunity to touch or otherwise sneak a coin into his pocket.
In Persona 4: Golden, the added S.link plotline with the main character's uncle's Bumbling Sidekick Adachi includes a scene where he demonstrates a magic trick that involves transporting a coin from his hand to the main character's pocket (from across a table they're sitting at opposite sides of).
The Adventures of Dr. McNinja. There's a flashback to Gordito's father, the Great Flying Shooting Juan (a sharpshooting trapeze artist magician) performing a card trick. The volunteer chooses a card, places it back in the deck, and throws the entire deck into the air. Juan shoots the card in midair... but the volunteer can't find the card afterwards. Then he gets a call on his cell phone...
Volunteer: That was the police. The man who robbed my house... they finally caught him because he was shot in the upper thigh... There was a queen of diamonds in his pocket.
Played with in an episode of Justice League that shows Zatanna performs for an audience with traditional illusions and stage tricks that fit this trope already, but then ends her show by using a real magic spell in order to keep people guessing how she really pulls off her acts.
What's New, Scooby-Doo?: The episode "Riva Ras Regas" centers around the ghost of the recently deceased stage magician Rufus Raucous, who turns out to have faked his death to get out of the spotlight and retire. He was last seen in a straitjacket nailed to a spinning wheel inside a building being demolishing by a wrecking ball, yet no explanation is given for how he survived other than "he's just that good", apparently. Later, when Rufus is encouraged by the gang to hold one more show to lure out the ghost, he perfoms tricks like being able to sprout new disembodied hands out of his sleeves, which walk around with a life of their own. How he does that isn't explained either, unless he invested millions in animatronics. The "ghost" of him can also fly, which turns out to be by magnets in its shoes, far more powerful than any real world magnet.
Stage magician David Copperfield tried to prove that these were possible. He once did a show (on TV, but with a live audience) in which he made a running gag of complaining about how people always ask him if his illusions are done with camera tricks. He insisted that they were not, and he wound up the show by doing a "real" camera trick, namely, he rolled a television camera onto the stage and made it disappear.
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