Everything Makes a Mushroom

1606. If my fireballs always form a mushroom cloud, time to tone it down a bit.

—Things Mr. Welch Is No Longer Allowed to Do In An RPG

The shape of a mushroom cloud is indelibly associated in everyone's minds with nuclear explosions. This trope is for explosions where that isn't the case—instead, the mushroom cloud is Played for Laughs, or just to show how powerful the explosive is.

It's worth noting that the mushroom cloud effect is not actually exclusive to nuclear weapons, it's just that nuclear weapons are far beyond the heat and explosive force required to cause the effect, and so the two became heavily associated with each other. In truth, it doesn't take very much explosive at all to form a mushroom cloud—you can create one with a couple dozen pounds of gunpowder.

Examples of Everything Makes a Mushroom include:

Anime And Manga

Ouran High School Host Club has Honey getting angry represented with a pink bunny mushroom cloud.

Films -- Animated

Over the Hedge has a scene where the cast open a bag of well-shaken cheesy puffs. Cue mushroom cloud visible from the moon.
Flint Lockwood gets a mushroom cloud in Cloudy with a Chance of Meatballs early in the movie.
In Chicken Run, an explosion of gravy looks an awful lot like a mushroom cloud.
During the opening sequence of Toy Story 3, a bomb dropped by Hamm's spaceship creates a mushroom cloud. Made of Monkeys. To be fair, the whole sequence takes place in Andy's imagination.
In How to Train Your Dragon, the impact of The Green Death into the ground results in a large mushroom cloud, which Hiccup and Toothless have to outrun.
In Atlantis: The Lost Empire, the characters at one point throw Cookie's greasy food into their campfire. The result is a miniature, oily-looking mushroom cloud. In a non-comedic example, the Viking Prologue Deleted Scene features an unlucky longship targeted by the Leviathan's Breath Weapon, resulting in a huge mushroom cloud of vaporized seawater and a few wooden splinters.

Films -- Live-Action

As previously mentioned, any powerful enough explosive will create a mushroom cloud, but few conventional explosive are that powerful. The Tall Boy bomb, as seen in Rambo, is one that is that powerful, something many internet "comedians" failed to realize when snarking about how Rambo should have been poisoned by nuclear fallout.

Literature

In the second book of Percy Jackson and The Olympians, Tyson and Percy, playing with chemicals, make a "orange mushroom cloud in the trash can."
The Gamma World choose-your-own-adventure book American Knights has a large conventional explosion create a mushroom cloud. The main character nearly has a heart attack before his sentient Powered Armor explains this trope to him.

Video Games

The Disgaea series is fond of having attacks produce these, sizes ranging from ones slightly bigger then a character to ones extending into outer space. Some recurring mushroom cloud producers include Zetta's Zetta Beam, the Dragon's Dragon Nova, and the Prinny's Pringer Beam.
Pretty much every conventional explosive, from TNT-rockets, to iron bombs in Command & Conquer: Red Alert 3 causes a small mushroom-shaped cloud to appear. And this is a setting in which nuclear weapons are specifically mentioned to have never been developed.
Ratchet and Clank 2 has the Mini Nuke, an explosive grenade that isn't nuclear.
Explosives in LittleBigPlanet create mushroom clouds in the background if you detonate many of them.
The Cain in Mass Effect 2 is specifically explained to not be nuclear in nature — it's simply a large, explosive-filled shell launched at relativistic velocities towards a target. Since the resulting impact is powerful enough to create the characteristic mushroom cloud, it's referred to as the 'Nuke Gun' by its users in-universe, and has radioactivity symbols plastered all over it.
- Presumably this is just clever product marketing by the Cain's manufacturers.
The Doom-Shroom from Plants vs. Zombies is a black, evil-looking mushroom that explodes in a mushroom cloud. Granted, the explosion is pretty big and instantly kills anything short of a Gargantuar, but it is definitely not nuclear in nature.
The E3 trailer for Super Smash Bros. Brawl (semi-)ended with Wario preparing his fart attack—whereupon the camera shifts to a remote view of a lime-green mushroom cloud.
In Tales of Phantasia, the strongest fire spell "Exploder" creates a large mushroom-shaped explosion of fire.
At the end of Mega Man 4, Dr. Wily's lab explodes in a skull-shaped mushroom cloud.
In Lemmings, the "Nuke" (explode all lemmings) icon.

Web Animation

When Strong Bad blows up the Tandy 400 in the Strong Bad Email "retirement" using the King of Town's denture-cleaning tablets, a bottle of Mountain Dew, and a pickaxe, the computer explodes in a pixellated mushroom cloud drawn in the same style as the Bad Graphics Ghost.

Western Animation — Television

In The Simpsons, Sideshow Bob take Bart and Lisa hostage next to a 50's A-bomb. His demands are refused, he pushes the detonator, and a mushroom cloud explodes... before the camera pans out to reveal the cloud is, at most, two inches tall. Sideshow Bob then comments that "he HAD to go for the retro charm".
In the episode "The Desert" of Avatar: The Last Airbender, Aang's airbending makes a mushroom cloud. Sokka, who is tripping on cactus juice, reacts hilariously:

Sokka: Friendly mushroom! Mushy, giant friend!

In the Futurama episode "Insane in the Mainframe", Malfunctioning Eddie is in the robot asylum because he explodes whenever he is told something surprising. When he's told he's being released, everyone tenses for an explosion, but all that happens is a tiny mushroom cloud erupts from his shoulder.
Since anything and everything explodes when thrown or handled roughly in Aqua Teen Hunger Force, mushroom clouds occasionally add a bit of emphasis.
Ditto on Jimmy Two-Shoes.
In Dan Vs. "Traffic," the explosives used to blow up a car lot make a mushroom cloud.
In My Little Pony Friendship Is Magic, Rainbow Dash makes a rainbow-colored mushroom cloud while helping to tear down Applejack's old barn in "Lesson Zero".