Sorcerer's Apprentice Plot

Someone only semi-qualified, the "apprentice", gets hold of the Phlebotinum when its normal user, the "wizard", is away. The apprentice uses it for his own advantage, but soon ends up with far too much of a good thing.

At the end of the episode the wizard returns and delivers a quick aesop, which may often degenerate into a Fantastic Aesop depending on how well it is delivered. Typically, it's either a hero misusing his mentor's phlebotinum or a Sidekick misusing that of the hero.

Often causes a Me's a Crowd or Literal Genie plot.

Named for the old story best known today from its appearance in Disney's Fantasia—Mickey Mouse, the Sorcerer's apprentice, uses his master's magic to bring a broom to life and make it fetch water for him. The broom obeys only too well, and soon the whole castle is flooded and the sorcerer is forced to (quite literally) bail Mickey out. The Disney version is originally based on a story by Lucian, written around 150 CE, so the trope itself is Older Than Feudalism.

Not to be confused with the 2010 film (though that does have an homage to the original Disney short, being also a Disney movie).

Examples of Sorcerer's Apprentice Plot include:

Comic Books

A distinctly adults-only version occurs in the XXXenophile story "The Sorceress' Appendage".
The Tales of the Green Lantern Corps story "The Apprentice" does this with the Green Lantern Ring.

Film

This is essentially the plot of Bruce Almighty.
The film Dragonslayer does this a bit differently. The apprentice is lazy and doesn't develop his magic. The sorcerer is out of the picture, the apprentice takes his jewel of power, and suddenly has all the same magical competence without having to work for it. Three guesses what happens later...
In the 2010 film of the same name, the literal sorcerer's apprentice Dave enchants mops to clean his lab while his master is away. It doesn't go so well. See the Fantasia example above.
From the silent movie The Golem: In the Rabbi's absence, his apprentice rashly revives the deactivated Golem, but soon loses control over him. The resulting rampage of the Golem is the movie's climax.

Literature

Trope Namer is Goethe's ballad "Der Zauberlehrling", made famous by Paul Dukas' Symphonic Poem L'apprenti sorcier, made still more famous by a certain mouse. Amazingly, considering that it went through not one but two transformations, the Disney adaptation is remarkably close to Goethe's original poem.
The plot for The Wednesday Wizard, where the apprentice to a wizard in the middle ages accidentally sends himself through time to the modern day (The Nineties). Other than slight amounts of magic, the middle ages was normal, thus leading to the apprentice's amazing discoveries in the 20th century. Upon returning, the wizard doesn't find out until the sequel book, when stories of things like "a dragon named Trayne" and "terrible beasts called Kars" getting loose give the apprentice away. Also in the sequel, the second main character - a girl from the present that the apprentice met - was transported back in time before the wizard found out, meaning the apprentice did this twice.
The Wild Bunch by Tom Dupree (Realms of Magic) had a rather ingenious use of almost unusable artifact.
Terry Pratchett's Mort follows the basic plotline of the Sorcerer's Apprentice: a young man becomes Death's apprentice, is left to his own devices, accidentally saves somebody's life, creating two conflicting realities that threaten the balance of cosmos, and Death is forced to step in to fix things, first intending to claim lives of everybody involved as punishment to Mort, but eventually relenting to a more merciful solution.
Basil St. Cloud has issues with this in The Fall of the Kings, but it's justified in that magic is just returning to the world.
In The Eyes of Kid Midas, Kevin Midas borrows Reality Warping sunglasses from a mountain (a stand-in for God). Things get pretty screwed up, but in the end, he gives the glasses back to the mountain and everything works out okay.
The first book of The Icewind Dale Trilogy has two examples of foolish apprentice wizards making a mess of things, one is tricked into murdering his master and ends up enthralled by the Shard, the other accidentally unleashes a Balor.

Live-Action TV

In the Torchwood episode "Everything Changes", all the Torchwood employees (except Ianto) are shown as bringing alien technology home for selfish use. While the technology itself works well, Tosh and Owen return their appropriated technology after Suzie, driven mad with desire for power over the Risen Mitten, commits suicide.
At one point in Warehouse 13, Claudia uses a lab coat that magnetizes her to climb up to a lightbulb that's come loose. It works too well and suddenly she finds herself stuck to a metal girder, with more and more metal objects (including a bicycle and Artie's glasses) attaching themselves to her; eventually she needs to get Artie's help to get down.

Video Games

Besides Fantasia, Mickey Mouse has done it again in Epic Mickey. Y'see, while the wizard was out, Mickey poked around and found a world for forgotten characters. He visited and had fun, but accidentally creates a monster while trying to put his own image into the world. Mickey erases the beast (briefly), spills paint and thinner on the world, and escapes. Years later, it comes back to bite him.
Similar to above, Mickey was said to have been Yen Sid's apprentice in Kingdom Hearts II.
- In Kingdom Hearts: Birth By Sleep, we get some more details, including Mickey having ran off with an object that let him travel through worlds...without even knowing how to operate it properly. And in the prologue, we see a remade clip from the original Fantasia segment: Mickey is struggling to keep afloat on a book in a flooded room, no doubt caused in the same was as in Fantasia.
Played with in Neverwinter Nights henchmen stories. The intellectual gnome sorcerer tells a story of his apprenticeship which starts as if it would be this played straight, then subverting it and being frankly astonished that the player would think he'd try to use his master's equipment without permission. Tomi's story, on the other hand, plays this completely straight as it is actually more of a retelling of the Disney version, in detail.

Web Original

In one Sunshine Warriors story, Arrowstar's nephew Ralph discovers his uncle's Powered Armor and takes it for a spin. He does okay for a little while, and actually manages to stop a crime without causing too much property damage. But then he accidentally hits the suits afterburners and puts himself into orbit. Luckily, he's rescued before the suit's oxygen supply runs out.

Western Animation

Jackie Chan Adventures had Jade's constant use of the talismans for mischief or honest attempts to help.
The various times the Dragons misused Shen Gon Wu for pranks or personal gain in Xiaolin Showdown.
In "Wubbzy's Magical Mess Up", Wubbzy borrows Moo Moo the Magician's wand while the latter is away from the shop and ends up creating a mess of chaos.
An episode of Timon and Pumbaa had this happen with Rafiki's nephew.
Pinky from the Pinky and The Brain segments of Animaniacs had done something like this in the 'The Brain's Apprentice' cartoon, parodying the Disney Sorcerer's Apprentice short.
Twilight Sparkle sort of deals with this. As the student of a Physical Goddess, she's capable of performing amazing feats of magic, but she often messes up and makes things worse. "Lesson Zero" in particular, she tries to create a problem she can solve by enchanting her old doll with a "Want It, Need It" spell that quickly affects everyone in town. The ensuing riot keeps her from disenchanting the doll. It isn't until Princess Celestia herself shows up that the problem is fixed. And just like the Trope Namer, she is not happy.
- And then there's the resultant fan works. "Twilight messes up a spell and Hilarity Ensues" is probably in the top three most common plot outlines.
Invoked in Code Lyoko, when Franz Hopper calls Jérémie "the sorcerer's apprentice" and accuses him of screwing up Lyoko and endangering his friends' lives by using untested technology. Actually, it's not Franz Hopper. The Big Bad is trying to get Jérémie out of the way so he can launch his latest Evil Plan.
- In a more general sense, Jérémie really is Franz' apprentice, though they rarely communicate during the show. He's taking control of Applied Phlebotinum that he didn't build and doesn't fully understand, and whenever he tries to develop something new, odds are better than even that he'll screw something up.
In the Avatar episode "The Deserter". Aang discovers a Firebending master and is eager to learn firebending. The master is reluctant because he knows Aang has not mastered water and earth (and true focus) yet. To start with baby steps, the master gives Aang a tiny leaf to burn a little. But an impatient Aang yearns to show off his potential and creates giant flames that badly burns Katara much to his horror.

Web Comics

In El Goonish Shive, a wizard apprentice whose master was killed by a werewolf created an enchanted artifact, to fix a man who killed this werewolf but was bitten in process. This thing... didn't exactly work as planned. In a later arc the same guy appeared personally and acted like "Didn't Think This Through" incarnate.

Every properly trained wizard has heard of Abraham, the idiot apprentice who recklessly enchanted a massive diamond instead of selling it to pay someone more skilled to fix his cursed noble friend.