Use of this in the most absurd ways possible is a major Running Gag on Aqua Teen Hunger Force. A specific example is that anything Master Shake throws will make a mini-explosion when it hits the ground (one has to wonder if it's a Super Power or something). The episode "Kidney Car" ends with Carl's head exploding after he has his car destroyed by Shake twice.
Meatwad: Why'd he do that?
Shake: Why wouldn't he?
In the golf videogame, Zombie Ninja Pro-Am, not only do most opponents explode when you hit them with a chainsaw or guitar chord them to death, but the golf ball you hit occasionally in between killing people Carl, robotic turkeys from the future, and machine-gun packing tulips? That golf ball will explode if it goes out of bounds, and detonate spectacularly when you finally get it in the hole, presumably a) because the shape of the hole focuses the blast or something but more likely b) Rule of Cool.
Avatar has also blown up a dam, Zuko's ship on multiple occasions, an abandoned Earth Kingdom city, anything with Combustion Man, anything involving the Day of Black Sun, and Zuko himself (when he practiced lightning bending). All of which just goes to show that you CAN, in fact, combine Stuff Blowing Up and a good plot in the same cartoon, and still come up with a Crowning Moment of Awesome for your animation studio with an extra-special dose of WIN.
Beast Wars, along with most of the Transformers cartoons, has a lot of explosions. At least one of the Transformers will be blown up in every episode.
Not counting Waspinator, who gets blown to bits in nearly every episode regardless.
Rather hilariously, there is actually a Transformer called Landmine. That's right. An alien robot with the name of an explosive.
The vast majority of episodes set within the DCAU end with the villain's hideout exploding, for reasons ranging from self-destruct devices to joy buzzers falling into loose wiring. On one of the Batman Beyond commentaries, the creators admitted that whenever they couldn't figure out how to end an episode, they'd just have a building blow up.
One example took place nearing the end of Bruce's reunion with Ra's al Ghul, who at this point should have racked up quite a bit of Genre Savvy and was smart enough to install automated fire extingishers into his lair. Unfortunately, once the fires are put out, Ra makes the critical mistake of pronouncing, "It's safe." Sure enough, one loose electrical wire strikes the Lazarus pit, resulting in... well, you know.
Mad Stan: You think this is a joke? Look around, Batman! Society's crumbling! And do you know why? Information overload, man! As a society we're drowning in a quagmire of vid-clips, e-mail, and sound bytes! We can't absorb it all! There's only one sane solution: BLOW IT UP!
An episode of The Fairly OddParents! opens with a displaced rooster crowing to signal the beginning of a new day. After Timmy wishes his life were like an action movie to get rid of the boredom, we reset the episode to the rooster, which explodes.
Family Guy loves to blow stuff up. One episode had Meg racing against an Amish guy on a horse and the pair falls off a cliff. The wagon explodes, then, after a moment of looking nervous, the horse explodes, despite having no signs of injury.
In an another episode, Brian and Stewie blow up a house. The explosion is shown from multiple angles.
Peter sticks dynamite in a watermelon to give to Meg, calls it a "thanks for being such a sweetie" watermelon, then runs out the room.
As the creators of the show have pointed out in commentaries, every episode of Futurama ends either with something blowing up or a courtroom scene. Occasionally both (That's not actually true by the way).
One episode has a scene where they're being chased by giant space wasps. One colides with the hive wall and bursts into a powerful explosion for no reason whatsoever.
Kaeloo: Given the fact that the characters have bazookas, missiles and bombs, this trope happens at least Once an Episode.
Whenever the supervillain Drakken's hideout doesn't get blown up, Kim Possible almost always remarks how unusual that is.
Well, it's tough to make cheese blow up. Even if it's the World's Biggest Block Of Cheese. That one just melted.
Looney Tunes just loves to repeat that same explosion animation whenever the opportunity calls for it. However, the most unique use of that animation is Three Little Bops, where the Big Bad Wolf attempts to blow up (rather than down) the brick house with a large stick of dynamite. To do this, he lights it up from afar (one of the pigs blew out his match when he tries lighting it on the doorstep), but as he rushes back to the brick house, the fuse runs out. Cue the oft-used explosion animation, but rather than move on to the black smoke phase, the animation remains in the red smoke, playing the beginning blast at different points of the screen to the beat of the music, until it finally moves on to the black smoke and the usual fade back to the main animation of the short.
The second act of the Mr. Bogus episode "Meet Mr. Bogus" had an example of this, where Bogus has to deal with a rogue vacuum cleaner that is running amok throughout the house, which leads to Bogus swinging all around the vacuum as it chases after him. This results in the vacuum tying itself up before exploding after a few seconds.
Also played with in the Dr. Ninja Baljeet and Doof'n'Puss Shows within a show, where during fight scenes, it would cut to footage of utterly random things exploding (a speed boat, a cruise ship, and a bowl of fruit come to this troper's mind).
Slightly justifiable as the shows were parodying old action shows.
At the end of The Powerpuff Girls episode "Twisted Sister", fourth Powerpuff Girl Bunny exploded because of the unstable ingredients the other Powerpuff Girls used to make her.
Parodied in a Robot Chicken sketch which features a fake trailer for "Michael Bay Presents: Explosions!" in which all sorts of things explode, including a seagull and a baby carriage.
MA BA SPLOOM!
Scooby-Doo! Mystery Incorporated absolutely loves this trope. There is only a minimal amount of episodes where nothing explodes. Roughly half of Crystal Cove has probably been destroyed by explosions by near the end of the second season! (Many buildings have blown up, propane gas has been ignited, a diesel locomotive explodes in a violent train wreck (caused by the villain blowing up a railroad bridge that sends the track line out of service), even the Mystery Machine although in the final episode, the Evil Entity being destroyed undoes all the damage and mayhem that had occurred during the series.)
Sealab 2021 features the Sealab blowing up in every episode.
The Simpsons loves to blow things up in ridiculous ways. One of the best occurs when Homer tries to cook Mr. Burns breakfast and everything he tries ends up bursting into flames, even a bowl of cereal.
Occurs in a similar and almost as frequent manner on South Park. One of the openings even boasts "MORE EXPLOSIONS!".
In the episode "Cartoon Wars" Kyle's big wheel goes flying off a cliff after a chase with Cartman. The toy bike breaks like a toy bike should until it hits the ground, when it promptly explodes for no reason.
And when they try to make a movie, Sandy gets a bit excessive with the fake explosions. 'Did somebody say boom?'
The Tick: "'Cause I'm the Evil Midnight Bomber What Bombs At Midnight! Boom, baby, BOOM!"
The "Pfish and Chip" cartoons on the What A Cartoon! Show were loaded with this, since they were about two Funny Animals who worked on the bomb squad of the Big City Police Department.
In an early episode of X-Men: Evolution, the team has just gotten their hands on a device that needs to be destroyed. Cyclops prepares to blow it up with his eye lasers, when Shadowcat suggests that she can just ruin the device by phasing through it. Everyone else looks at her like she's crazy.