Mickey Mouse does this in The Little Whirlwind, by taking out and putting away a hammer just as big as he is.
Specific example
Adventures of Sonic the Hedgehog: Being an absurdist comedy inspired by works like Looney Tunes, various characters use this for comedic effect. Sonic in particular does it almost Once an Episode, using a disguise to cleverly trick Scratch and Grounder. Beyond disguises, Sonic also often utilizes this to conjure whatever object he wants, apparently so long as it aligns to a disguise. He ends up using this to save his or someone else's life more than a few times. Tails even uses it infrequently for disguises, usually alongside Sonic but sometimes on his own, making it almost seem like a skill he's gradually learning how to do.
Aladdin: Abu can hold any amount of stolen money, jewelry, fruit, and even Genie's lamp inside his vest.
Wakko from Animaniacs has a "gag bag" that contains anything, of any size, that he needs for the punchline.
In the Archer episode "Skorpio", Archer, naked after a rather messy three-way sexual encounter, literally pulls a grenade out of nowhere to throw at some mooks. This is even (literally) lampshaded immediately afterward, when Lana asks him where he got the grenade, and he responds by saying that "It was hanging from the lampshade!"
Hanna-Barbera's Captain Caveman has a Bottomless Magazine of objects and creatures he can pull from his body-length body hair, from a skeleton key to a large bone barbell (which he presses with ease). He even pulls things that are far larger than he is out of it sometimes, like a large dinosaur that he and his friends use like a stairway.
From Chip 'n Dale: Rescue Rangers, after Gadget luckily has a glass cutter to free the trapped heroes that she gets from Hammerspace. The glass cutter is taller than she is.
Monty: Do you always carry a glass cutter around with ya?
Gadget: No, only when I wanna cut glass.
In Count Duckula, Nanny was able to produce any item from inside her sling.
Courage the Cowardly Dog revels in this. At least five times in a single episode, characters will pull oversized items (giant mallets, giant masks, even loose change the size of frisbees) out of their pockets or from behind their backs. In fact, every cartoon Jon Dilworth has made does this.
Batman: The Animated Series: While not referenced exactly, Batman's utility belt is notoriously thin in appearance. Yet he somehow manages to carry a diverse array of equipment including several feet of rope/cable, His grappling gun which is wider than his belt yet fits in a pouch, fixed blade batarangs larger than the belts width, various electronic devices. The rebooted series slightly addressed this by designing his belt with larger compartments and pouches.
The Joker from The Batman/Superman Movie: World's Finest has him pull a big, freaking dragon-sculpted statue of Kryptonite concealed from behind his slender back.
Likewise, Harley Quinn, as the Decoy Damsel, demonstrates hammerspace by whipping out the comically oversized mallet to beat an unsuspecting Robin in Batman Beyond: Return of the Joker.
No matter how many times Tucker's PDA gets destroyed during the plot, he always has another one ready next time. In the 3rd episode, Sam asks him, "How many of those things do you have?"
Then there is the Fenton Thermos. Sure, sometimes Sam or Tucker will arrive on the scene just as Danny decides he needs one, and the animators may feel adventurous enough to show him carrying it on his back, but on most occasions this thing comes out of nowhere. It is unclear how many Fenton Thermoses the Fenton family actually owns. Considering the Fentons have a weapons vault, it's probably fair to assume that they have mass produced the Fenton Thermos. They are Crazy-Prepared for ghosts, after all.
A strange variation of this happens with Danny's alter ego. In one episode, Danny walks out his front door with his backpack on and transforms into his ghost half to fly to school. The backpack just disappears (until he turns back into his human half, that is)(this can also be applied to his outfit when he switches from one form to another).
In the same episode, he pulls a piece of toast out of nowhere in ghost mode.
Considering that Dora the Explorer is formatted in a style reminiscent to a point-and-click adventure computer game, the fact that Backpack is able to carry more than it can logically hold is a possible Homage to this trope. Its Spin-Off, Go, Diego, Go!, also does this with its own inventory character, Rescue Pack.
Dragon Tales: The dragons have marsupial-like pouches in which they can store just about anything.
Example when the gang is hiding everything for Ord's surprise party:
Zak: Where you gonna hide the cake, Wheezie? (Wheezie stuffs the cake into Zak's side of the pouch, and a squishing sound is heard) Eww! That feels gross!
Lampshaded in Drawn Together when Wooldoor says he keeps things in his fanny so he can "pull them out for comedic effect".
Duckman: When Cornfed reminds Duckman that everyone in town is working only a half-day (due to a civil defence drill that our antihero didn't hear about), Duckman says, "Ohhh, it's one of those days," and throws on — pulled out of nowhere and in a fraction of a second — an ultra-Orthodox Hasidic Jew's black hat, coat, and sidelocks. (Cornfed's response, just for the record: "Duckman, this isn't one of those days where you have to pretend you're Jewish.")
Done countless times in Ed, Edd n Eddy, with examples being Kevin pulling out a bike from his pants in "See No Ed", Rolf pulling out a giant hammer out to hammer Double-D into the ground in "Momma's Little Ed" and in "A Fistfull of Ed" with Eddy pulling out hotdogs and eating them (the kids even start asking themselves where Eddy got all those hotdogs in the first place).
Emily and the Baba Yaga: When Emily first finds the chainsaw, she pulls a can of oil out of nowhere.
In various superhero-themed episodes of The Fairly OddParents!, it should be noted that Timmy's Cleft the Boy Chin Wonder costume includes a faux chin attachment called a "utility cleft". And it can store a baseball glove, a plane, and a rocket. ALL LARGER THAN TIMMY HIMSELF!
Stewie Griffin pulls a variety of weapons out, including disassembled sniper rifles, machetes and ray guns. He's never seen putting them back, though, just throwing them off-screen when finished.
In a rare lethal example, his evil clone from Season 9 uses Hammerspace weapons to kill multiple people. Including the Kool-Aid Man with a literal giant hammer, after tricking him into crashing through a wall in his signature move.
In an early episode, Stewie used a Hammerspace ray-gun to kill himself from the future. After his future self saved him from his own Hammerspace bomb.
Aloysius Pig of Garfield and Friends' B-segment, U.S. Acres, can pull items from the back of his jacket, despite not having a pocket on the back. He only did it twice: once for a picture of smiley faces (which he called a whole staff of artists) and the other time for his business card.
Agent Six from Generator Rex keeps fold-out katanas in his sleeves. He also periodically produces throwing knives seemingly from thin air, but at least those are pocket-sized.
Louis "Sweet Lou" Dunbar of the Harlem Globetrotters. If you need something, he's probably got it stored in his 'fro.
Heckle and Jeckle are locked in prison in the cartoon "Super Salesmen." Prison guard Dimwit discovers Heckle using a metal file to try to escape, so he confiscates it. Heckle takes another file out of his prison cap, which Dimwit grabs, followed by a succession of files. Dimwit grabs the hat, turns it over, and whole pile of files pours out.
In Inspector Gadget and Gadget Boy & Heather, Gadget's hats always has the right tool (even when it's the wrong tool) for the job. The hammerspace is cranked up to eleven often when all of his gadgets deploy at the same time.
The characters of Kaeloo can pull random objects, as well as actual hammers, from behind their backs.
Ron from Kim Possible pulls a pickaxe out of nowhere in "Cap'n Drakken". Where Kim keeps her PDA-like Kimmunicator, even in her cheer costume (which evidently doesn't even have pockets), is equally mysterious.
Let's Go Luna!: Carmen always summons the Magic Globe from out of nowhere.
In The Little Rascals episode "Rascals' Revenge", as the Rascals are about to enter the abandoned house, Buckwheat produces a firefly-powered flashlight from inside his shirt.
On Lou and Lou: Safety Patrol, both Lou and his sister Louise (also known as simply "Lou") are capable of producing an orange cone that tags a "safety violation" seemingly from nowhere and then making it disappear.
The characters in Men in Black: The Series sometimes pulled some ridiculously large weapons from under their suit-coats. In one episode an MIB not only drew a large weapon for himself, but then pulled out another to toss to an unarmed comrade. Except for J, who always has just the noisy cricket, and sometimes a "silencer" that's bigger than the little gun.
Clancy carries around a duffel bag that contains, among other things, a pyramid, an ancient Greek temple, a Rubiks cube, and a pool stick. One episode has him entering it to fix something and it's an entire world in there.
Glasses Man stashes billiard balls and weapons in his dog's fur. In later episodes, viewers see that the dog's fur contains a parallel universe.
The eponymous character of Mr. Bogus seems to keep an unlimited supply of assorted items in the pockets of his pants, given the occasion that he would reach into his pockets for an item that befits his current situation.
My Life as a Teenage Robot: Jenny is probably the poster girl of this trope for robots. She has so much arsenal inside her body it would probably take all day to go though it all...
It frequently features the use of hammerspace by ponies, but mostly in small ways. Pinkie Pie, however, very frequently produces things out of Hammerspace, though Rarity has a slight tendency towards it, especially with her drama couch (for her to fall on; pulled on from just offscreen) in Lesson Zero. Spike occasionally digs around in his pockets for some items, even though he doesn't wear clothes, and in one instance pulls an umbrella out of nowhere after melting a massive hunk of ice.
Spike also has a justified example with his dragon breath. It's normally used to send messages to and from Princess Celestia, but in Spike At Your Service he uses it to produce his "Spike The Dragon Code" card. Whether he's actively able to store items or merely brought it from elsewhere is never addressed, but it's used as this all the same.
The Octonauts' breathing helmets disappear into their collars when a button is pressed, and the Octopod's launch bay doesn't seem nearly big enough to hold all twenty-six of the GUPs.
On Peg + Cat, Peg pulls her guitar out of nowhere to perform the "Problem Solved" song.
on The Penguins of Madagascar this is done by Rico almost constantly. It starts off as a paperclip in Madagascarbut throughout the show he vomits up chainsaws, bombs, and a Higgs-Boson particle, among many many many other things. In one episode Mort has to get something from inside Rico and Kowalski tells him to take the elevator. It's faster.
The episode "The Chronicles of Meap", lampshades it when Candace calls out adorable alien Meap on "where he keeps all those pictures" he uses to communicate.
This was lampshaded further in the character commentary for the episode. Monogram is wondering the same thing, but Doof isn't that surprised:
Doofenshmirtz: You know, I find that in this particular reality, I can pull anything out from behind my back.
Similarly, Perry's hat simply appears and vanishes most of the time.
Many times, Agent P (Perry the Platypus when on duty) is able to retrieve items by reaching behind his back.
So that he can play a part in the "Ain't Got Rhythm" musical number without needing to actually say anything, Ferb keeps just having instruments in the form of a tambourine, guitar and trumpet, all of which he plays perfectly, and which he is able to instantly change between shots so that he's playing whichever is more prominent in the mix at any given time. Now, he does pick up a pencil holder from Sherman's desk to use as an improvised instrument, which does make sense...except that it wasn't there three seconds previously, before the camera cut to Sherman.
In the cartoon series Popples, hammerspace is at their beck and call when they reach into the pouches on their backs, especially when the Rule of Funny is applied.
On The Hub'sPound Puppies, the dogs present new adoptees with collars as a parting gift, and quite often, they do so away from the pound itself. The team could be pulling them out of their fur, however, all of them have presented collars. Only two of the five members are shaggy enough to possibly hide a collar in their fur out of view, with only one of the five not having a visible collar of his own.
Razzberry Jazzberry Jam has characters frequently produce items from nowhere. The most commonly-conjured items are Buddy and Krupa’s drumsticks, and the most egregious case was when, in “Bongo Mania”, Nestor and Cesar produce a box of records bigger than they are, and which they would have had no reason to carry around, from behind their back.
Ready Jet Go!: Sunspot pulls objects out of thin air multiple times, one of his many talents. For example, in "Detective Mindy", Sunspot pulls several sunglasses out of nowhere.
Shag from Road Rovers seems to have access to hammerspace inside his immense coat of fur. Colleen was even able to sneak into one of Parvo's bases hiding in his fur.
Sam & Max is guilty of this. A special mention goes to:
Sam: Max, I didn't know you were a marsupial!
Max: Me neither! Whatever that is...
Also a Running Gag from the original comic and throughout the adventure games.
Shaun the Sheep: Shirley, the fat sheep, has a fleece which serves as Hammerspace. On one occasion it was found to contain chocolate, an aerosol of cream, and a large jelly on a plate.
The characters in Shirt Tales were capable of pulling random items out from under their shirts until something useful popped up.
In Scooby-Doo and Scrappy-Doo, the title characters made use of this trope occasionally. An example that stood out was in the second episode, "The Night Ghoul Of Wonderworld" Scrappy knocked over a knight. He walks off screen and returns moments later with a carjack, stands the knight back up and the carjack is never seen or referenced again.
Marge's hair appears to contain hammerspace, as she has retrieved various items from it. On one occasion whilst swaying from side to side doing exercises, each change in direction dropped a larger item out of her hair.
Krusty's small car can also transport several clowns, each wearing oversize footwear.
In Sonic Boom, Amy is able to pull out her trademark hammer whenever she wants, despite the fact that it's almost as big as she is.
In episode "Fear of a Krabby Patty," a frantic, delusional SpongeBob gives Plankton just enough time to squeak out, "Hey where'd you get that piano?" Just before, well, you know.
Plankton did one of these himself in his debut, "Plankton!", offering SpongeBob a golden spatula in an attempt to get a Krabby Patty from him. "I've been keeping it in my...secret compartment. SHING! Sparkle-sparkle."
In "FUN", where he learned FUN from SpongeBob, Plankton managed to hide the Krabby Patty in his pocket. How does he even have a pocket, let alone hide something more than two times his size?
In "Christmas Who?" SpongeBob grabs pencils, paper and a photo frame from nowhere.
In "Dying for Pie", SpongeBob places the rather large pie-bomb in his tiny pocket, leading Squidward to think he had eaten it and had only hours left to live.
In "Kracked Krabs", Mr. Krabs and SpongeBob manage to stuff themselves into an envelope for the Cheapskate Convention, resulting in it rather heavy to carry. One of the cheapskate crabs also stuffs himself inside one of Mr. Krabs' suitcases.
In "Krusty Kleaners", SpongeBob somehow manages to keep a pogo stick stuffed inside his own shoe.
Taz-Mania used many of the tropes from the Looney Tunes shorts, so Hammerspace was well and truly in effect. In "A Flea for Me", for example, the flea pulls a complete oil well out from under his coat.
Lampshaded in an episode of Timon & Pumbaa, where the title characters fall off a cliff and pull increasingly ludicrously large items — pianos, elephants, cruise ships — from behind their backs ("You never know what might happen to be just behind our backs!") while Rummage Failing for a parachute.
Wreck-Gar in Transformers: Animated has his trash bin, that functions as both Hammerspace and a "Pit of No Return". He can take many useful (and more useless) items from it, and things that are put in it seem to just disappear. Swindle's chest compartment does the same thing, except it canonically links to a hammerspace.
In Transformers parlance, hammerspace is known as subspace and is used for a number of things, including weapons storage and a place to shunt mass when transforming into something tiny (for instance, when Megatron becomes a gun). And yes, this is also where Prime's trailer goes; scenes are choreographed so it just conveniently moves offscreen when he shifts to robot form, only appearing if he needs it. (Like in this scene.) And long before being largely canonised as subspace, this mysterious dimension was actually known to many fans as "Trailerland".
Some continuities from different writers (mostly the comics) have been attempted to justify it with actual talk of mass shifting technology, but in the end it is just A Wizard Did It. The Transformers films did everything it could to avoid this, with appropriate vehicle modes to accommodate robot modes (with debate about Frenzy's head turning into a cell phone). In fact the All Spark as being capable of this was presented as a very unique and special thing it can do.
The Minicons (at least in the Cybertron series) seem to have the inverse of their larger counterparts. In their vehicle modes they are nearly the same size as any other Transformer, granted a tad smaller; Jolt in particular stands at least 10 feet tall in his helicopter mode and has enough room inside for two full-size adults to ride along. In his robot form, Jolt rivals the kids in height and can not only enter houses, but one episode had him hiding in a closet with another Minicon of the same size! Their cockpits seem to function like this as well. When Vector Prime finds Atlantis the kids use the Minicons to travel underwater; the Minicons transform into their robot modes underwater while the kids are still inside them, apparently with plenty of room for them to gesture wildly when startled. It isn't until later when VP drains the water out of the city that the kids come out by just walking out from behind the robots which are at head level.
During the second season of X-Men: The Animated Series, after having lost his ultimate telepathic powers, Professor Xavier is able to produce weapons instantaneously in order to save Magneto, including a boomerang, and a spear!
Gorga, the pet alien dog from Zula Patrol, has a Hammerspace up its nose! Or is that its mouth?
under "I Am the Very Model of a Cartoon Individual").