This gets a nice lampshade in Mickey, Donald, Goofy: The Three Musketeers, when Donald tries to warn Mickey that Pete's evil... Donald says the entirety of the warning, with Pluto and Mickey watching, the camera turns to them, they do a Double Take to each other, then Mickey says, "Donald, I have no idea what you're saying."
Dr. Drakken from Kim Possible often drops into this when mocked by his sidekick.
Shego: Dr D!
Shego: (deadpan) You've stopped using words.
In the Tiny Toon Adventures episode Wacko World Of Sports, Buster and Babs are sent flying into a trash container by an angered group of people. Upon digging himself out, Buster starts swearing in Angrish until Babs empties a bucket of water onto him.
"No, Squidward, we've already played Babble Like An Idiot!"
Also, Mrs. Puff says SpongeBob has a very 'colorful vocabulary' after said sponge spouts spiraling smashy random words about Mr. Krabs and his monetary greed, something unintelligible, and Mrs. Puff looks shocked after flipping through a pocket dictionary to find out what he says.
To be fair, in another episode the local cursing technique is a small 13 variety of naval sounds. Makes you wonder why the heck that ancient dolphin warrior (later episode, differing season,) wasn't being treated as cursing his head off after the volcanic explosion, considering the substandard annoyance of the cursing (Lampshade Hanging) episode is a dolphin sound. The cursing episode ends with Mr. Krab's MOTHER saying a jalopy sound after hitting a similar rock to the earlier curse-initiating rock. Luckily it was just another car horn of the local Mr. Jenkins (in fact, if you read her lips carefully, you'll see that she's saying "My poor old foot!").
Either played straight or subverted with the Tasmanian Devil, a creature who seems in a perpetual state of being pissed off. He spit-growls, rages, and roars constantly, though has proven to be able to speak coherently when very angry. "What for you bury me in the cold, cold ground?"
And sometimes he gets so angry he becomes reduced to jumping up and down and growling like a demented gorilla.
Hilarious example on The Simpsons, "$pringfield, or How I Learned to Stop Worrying and Love Legalized Gambling", when Homer confronts Marge about her gambling addiction.
Homer: [grabbing Marge] Jergiddaberdareddaarra!
Marge: Homer, what is it? Slow down!
Homer: [slowly] Jer gidda berda redda arra.
Marge: Think before you say each word.
Homer: You broke a promise to your child!
Also from the Simpsons, in a flashback when Edna Krabappel breaks up with Moe.
After a Raiders of the Lost Ark shoutout where Bart steals a penny jar from Homer, he escapes onto the school bus while Homer, still in his underwear, screams and gibbers hysterically as it drives away.
After eating the poisonous Fugu fish, Dr. Hibbert explains the 5 stages of Death Anxiety to Homer. The 2nd is anger, to which Homer responds by yelling at Hibbert "WHY YOU LITTLE-! DEH,DOOOOH,YAHYUH!"
And don't forget Ned Flanders. His psychologist even explains that a treatment he received as a child to make him behave better (spanking) worked too well and so, whenever he felt anger, he could only express it by spouting a chain of incoherent made-up words.
"Well I'll be darn-diddly-arned." "Whoa, now, steady on there. I'm here to help, you know."
Flanders: Calm down, Neddly diddily diddily diddily, doodily. They did their best shodaiddily iddily iddily diddily diddily. Gotta be nice, hostidididildilidilly... aw, hell-diddly-ding-dong crap! Can't you morons do anything right?!
When Moe does this, he refers it as "choking on his own rage".
Also, Sokka, when Aang and Toph wake him up from some well-earned rest. He gets up in his sleeping bag, hops over to Aang, babbles unintelligibly at him, hops over to Toph and babbles at her, then hops off, jibbering something that sounds like, "I'm talking and using words!"
Zorak in the Space Ghost Coast to Coast episode "Flipmode". A gas leak has cauased the cast to act crazy(er), and Zorak eventually takes refuge in vent. While trying to get him out, Space Ghost gets trapped in the pipe as well. Zorak starts to freak out, screaming at him to get out, and starts to shout gibberish.
Bender does this a lot in Futurama. One particularly funny instance occurs in the second "Reincarnation" short where his enraged grunts are accompanied by visual Swear Symbols and his body flashing red.
Fry, in "How Hermes Requisitioned His Groove Back", manages to lose even more of his graspof the English language than usual when Bender has his eccentric personality forcefully removed and downloaded to a diskette. He can only manically exclaim "But, Bender! Need brain!... For smartmaking!" to the bureaucrat who did it.
"What did you do now? STOP DOING THINGS!"
Hermes (after contemplating jumping off the planet express building): "Sweet something, of someplace."
"Professor! Lava! Hot!"
Professor Farnsworth built an angry dome for being angry in. In the episode in which it appears he paces back and forth beneath the transparent dome muttering in Angrish.
The Peanuts Easter special has Peppermint Patty speak Angrish after she tells Marcie to get the eggs ready to be decorated and she fries them. Peppermint Patty falls back on the good old fashioned "AAAUGH!" when Marcie cooks eggs in the waffle iron, attempts to toast or bake them and finally make egg soup.
Producer: Hoyle! How'd you... with the going... you were there, but here now, you are, for me to see... How'd ya do?
Yakko: What'd he say?
Wakko: *mocking* Hoyle! How'd you... with the going... you were there, but here now, you are, for me to see... How'd ya do?
In one sketch where Dot had trouble pronouncing her Overly-Long Name, she eventually flipped out and began stomping around in circles, venting an incoherent rant dotted with Sound Effect Bleeps.
In the Fast Forward episode "Timing Is Everything", Donatello gets the shocked version when he and Splinter go back in time to the accident that produced him:
Donatello: Was that... did we just... were those... us?! Did I just see... my own creation? Aaah!
Splinter: Deep breaths, my son, deep breaths.
It's revealed as a gag in Chowder that Schnitzel's normal speech of "radda radda radda" is just a long stream of angrish due to always being tense and frustrated.
In one episode of The Powerpuff Girls where the girls learn not to use profanity, they end up fighting a giant lizard monster that has a toilet for a head and speaks entirely in this.
Yellow Submarine - Old Fred flees the invasion of his home land and finds himself in Liverpool, at the home of The Beatles. He passionately tells his plight in a stream of incomprehensible babble, ending in "Blue Meanieeees!!!", telling it to each band member in turn, exactly the same way, so by the third telling, Ringo and John join in on "Blue Meanieeees!!!"
George: (to John and Ringo) Ah, you're nuts, the pair o' ya!
At the end of "A Glitch Is A Glitch," Princess Bubblegum degenerates into this as she destroys the Ice King's computer.
In the Adventures Of Super Mario Bros 3 episode "Never Koop a Koopa", King Koopa finally has the heroes in the position to have Princess Toadstool sign away her kingdom to him. the Princess manages to delay the transfer by asking him to order a press conference, and when he leaves his son Cheatsy (Larry) tries to get her to sign the kingdom to him. In the resulting confusion, the good guys escape, leaving a furious Koopa to chase Cheatsy around his throne bellowing.