A character opens a surreptitiously bulging door to a storage area, and is buried in an avalanche of junk, followed by a skier or something if the authors are feeling particularly silly.
The set-up may often involve another character trying to clean up in a hurry (and by "clean up", we mean "just hide all the mess somewhere").
If the closet is continuously left in complete and utter chaos as a Running Gag, no one will bother to organize this closet, and instead opt to quickly open it, retrieve what they need, and hastily shut it in one smooth movement.
Later, a character who is oblivious of the closet's nature innocently opens it, only to be buried under a heap of cleaning tools, souvenirs, novelties and whatnot.
Apparently, all household junk is rubbery and spongy enough that you can squeeze a roomful of the stuff into a single foot-deep closet, as long as you're strong enough to force the door shut afterward. Given the fact that many of these knickknacks can be comfortably squeezed into (and pulled out of) thin air, this may not be that inexplicable.
Alternatively, the closet could just be really large on the inside.
Sometimes Truth in Television.
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A commercial for Rubbermaid food containers emphasized how one could keep their containers nicely organized versus other brands, demonstrated with an exploding kitchen cupboard full of Ziploc-esque containers.
In ROD The TV, this happens with the three sisters' entire apartment, which is stuffed to bursting with books.
Happens in the very first episode of Mahoromatic, where Mahoro opens a bulging closet in Suguru's house only to promptly have an avalanche of matching shorts spill out all over her.
The Ranma ˝ anime episode featuring the return of Principal Kunō to Fūrinkan High School has an office filled to the brink with coconuts, which crash upon the students as soon as they open the door.
A minor Running Gag in Belgian comic Gaston Lagaffe. We are once shown Gaston's technique for filling the dreaded cabinet so that things don't fall out: he lays it down and quite literally shovels everything in.
In the comic Suske en Wiske, the girl Wiske is Genre Savvy (or perhaps just knows the habits of the people she lives with): before opening a medicine cabinet, she places a basin before it and stands back, as the contents falls out of it.
In Calvin And Hobbes, Calvin uses this trope to make it look like he cleaned his room — until his mom opens the closet.
Calvin's Mom: Back to work, kiddo. Calvin: YOU made THIS mess! YOU clean it up!
A Running Gag in the newspaper strip Big Nate, with Nate's school locker exploding with an impossible volume of crap whenever he opens it (with Nate able to swiftly find whatever he wants to in the debris).
Happen with the Wardrobe in Epic Movie. Or so it shows in the commercial.
The "broom closet" Hoggle opens accidentally in the oubliette in Labyrinth is packed full of stuff. However, since opening the door from the other side revealed a passage, that closet obviously wasn't following the laws of physics.
Happened once in, of all places, Star Trek: The Original Series, episode "The Trouble with Tribbles", resulting in Kirk being buried in an avalanche of tribbles. Certainly embodies the spirit of the trope, but also justified in that the "closet" in question was a (formerly) grain-filled cargo bay.
The fact that tribbles are still falling on Kirk's head after the trap is open is explained somewhat in the Deep Space Nine episode "Trial and Tribble-ations", when it is revealed that the tribbles are being thrown out onto him by people trying to identify which one is a bomb.
Zoboomafoo: Whenever the Kratt Brothers want to go on an adventure, they open the closet and just shield themselves from the falling safari gear. Then they pick up what they need from whatever fell on the ground and leave. Also subverted, as a female guest-host who occasionally visited was able to open the closet, take out what she wanted, and close it again, without any problem. Of course, the next time the guys opened the closet, they again had all their stuff raining down on them.
In an episode of Friends, Ross and Monica are cleaning out their dead grandmother's apartment. Earlier on they had had a discussion about how their grandmother was always collecting packets of sugar. Ross pulls down a box from a high shelf, and out spill piles of sugar packets.
In an episode, Spencer is going on a camping trip and needs to get his sleeping bag out of the Shays' storage locker in the basement. Guess what happens next.
In another, Sam rigs Lewbert's cupboards to bury him with golf balls.
Used twice in one episode of Three's Company when the gang goes on a trip to a cabin. Trying to find the bedroom, Jack opens a door which actually leads outside and is bombarded by a pile of firewood. Janet opens the closet and... you know the rest.
A Saturday Night Live skit involving a couple of water delivery men who have been hoarding their product ends with one of them opening a closet door and a cascade of empty water jugs spilling out.
An episode of The Dick Van Dyke Show has Rob imagining the world has been taken over by aliens through the use of walnuts (it's a long story). The episode climaxes with Rob opening open a hall closet and a ton of walnuts cascading out...followed by his wife Laura.
Sam And Max Freelance Police: Sam and Max take a little souvenir from every case they do, and keep it in the closet. Once they get to the future and try to open the closet, Sam has to slam it shut before he's crushed under all that stuff.
Used early, when Agatha cleans up a lab by stuffing a nearby closet with all the junk, and then the overlord's son Gilgamesh decides to open it to get something. ("That's the worst filing system I've ever seen.") The bump on the head actually helps him clear up his thoughts.
It's also used in a wallpaper that shows Agatha, Gilgamesh, and Tarvek housecleaning; Krosp has just opened a door and a huge pile of skulls have fallen out. The featherduster Agatha's holding seems rather inadequate to the task ahead....
A Running Gag in Tennessee Tuxedo And His Tales, where everytime Mr. Whoopee gets the 3DBB he has to open the storage, which leads to the character getting avalanched with all the junk he keeps in there. He always comes out unharmed with the blackboard he was looking for.
In the short Fool Coverage, insurance salesman Daffy Duck rigs up one of these to convince Porky Pig he needs to buy a policy. Naturally, it backfires and Daffy's the one who ends up buried in junk.
In Thumb Fun, Daffy overstuffs the trunk of Porky's car to similar effect... and it, too, backfires on Daffy!
Literal exploding closets are utilized in some shorts, as when a character finds himself in a dark closet and lights a match only to find it is filled with explosives, with predictable results.
In The Simpsons episode "Supercalifragilisticexpeali(Annoyed Grunt)cious", after Sharry and Bart and Lisa clean up the room by shoving everything in the closet, under the bed and under the rug, as soon as they close the door, everything spills back out, making the room messier than it started out.
Codename Kids Next Door has the entire plot of an episode revolving around this. It takes the Bigger on the Inside variant to extremes with the avalanche being from a literal Himalayan-themed mountain of junk inside the closet.
This happens in the Code Lyoko episode "Sabotage", where Jérémie has to tidy up his room in a hurry for an inspection. Jim needn't even touch the closet: it bursts open each time he gets close to it.
SpongeBob SquarePants has a closet full of trophies. Patrick ended up opening it in one episode, and was flooded by the trophies inside.