The show does it purely for laughs, primarily because the characters doing most of the cussing are fourth-graders (the only exception to this is Butters). The episode "It Hits the Fan" left "the s word" uncensored and featured a counter for how many times it was said. It ended at 162. Virtually every sentence uttered by Kenny contains the word fuck. Of course his speech is muffled so that the only word you don't have trouble understanding is fuck.
Depending on who is talking on The Boondocks this can happen, ironically enough by the white people on the show more that the black people (even though the two white people who do so are voiced by Charlie Murphy and Sam Motherfuckin' Jackson himself).
Also, the rare Cluster S Bomb was done by Tom Dubois, of all people.
Riley has a pretty epic one in 'The Fund Raiser'.
The Oblongs: "How could I have been such a fiddly faddly fool!? Excuse the string of F-words. Subverted, of course.
A gag on Bromwell High had one of the main characters doing a piece on the sitar for the school's music night. The girl then goes to her friends for commentaries. One of them pulls out an S Bomb, so to speak.
Natella: Well? What did you think? Give me your honest opinion. Keisha: You were shit. Shitter than shit. You were so shit that it made me want to block up my ears with shit, then eat some shit, and then do a shit. Natella: Right. Latrina? Latrina: shit.
On Drawn Together, the characters toast to freedom of speech ("Fuck yeah!" "It's the shit!"). Captain Hero then rips off his pants and says "I wanna fuck the head off a fucking pig and then rip its fucking guts out and then fuck its fuck fuckity fuck fuck fuck fuck fucky fuck fuck fuck fuck "
Aqua Teen Hunger Force gives us pregnant Meatwad (with every profanity censored with a random noise, accompanied by a red X when each profanity is censored).
Meatwad: Whoa... boy I apologize. My hormones are going nuts! Now please... if you would... Get the fuck out of my way. I mean how many times do I have to gotta fucking write "ice cream" on this fucking list before someone gets his shit in gear and brings home some fucking ice cream? Maybe I should get a STEAK KNIFE, and etch it in your motherfucking forehead! HOW HARD CAN IT FUCKING BE? ICE-MOTHERFUCKING-CREAM! I guess that's the price I pay for living with two fucking MORONS! Shake:...What happened to courtesy? Did it just... disappear?
For an example not from a main character, there's the creepy one-shot appearance by Glenn Danzig, who bought Carl's house when it was filling up with elf blood. While interrogating Shake as to where the Cybernetic Ghost of Christmas Past from the Future is
Danzig: Now listen to me as hard as you fucking can. The fucking robot came with the fucking house and now it's fucking gone!
In Home Movies, the episodes "Coffins and Cradles" and "Curses" have tons of swearing mostly by Brendon, Coach McGuirk, and Linda.
There was an episode of Dexter's Laboratory, "Rude Removal", in which Dexter accidentally made evil twins of himself and DeeDee. This episode has only been shown at panels at animation conventions because of all the rude language that ensues. Adult Swim eventually released the episode and now it can be easily located.
Animaniacs of all things had a moment where girly Dot burst into a string of (bleeped of course) profanities upon messing up her introduction one too many times. Yakko proudly says, "That's my cute little sister who said that. Good night, everybody!"
Tiny Toon Adventures had a character named Foulmouth who frequently go into Cluster (Bleep) Bombs whenever enraged (which was pretty much constantly).
The episode "Sailor Mouth". Sure, it was bleeped by dolphin noises, but it's obvious "fuck" was the intended word since it fit so neatly into their sentences. The episode was pretty much a parody of this—why else would Patrick refer to the words as "sentence enhancers"?
Interestingly enough, there's a scene where Squidward whispers the word twice to Mr. Krabs and it sounds like he's saying something like "tennysaw".
At the end of "Krusty Love", SpongeBob lets out a stream of gibberish that is obviously intended to be interpreted as cursing.
Mrs. Puff: I had no idea Spongebob had such a colourful vocabulary! Mr. Krabs:(Gaping in shocked silence with his jaw on the ground)
In the movie Tarzoon: Shame of the Jungle the character Brutish uses the word in nearly all his sentences even as he's been eaten alive and dying in his final breath he says "the goddamn fucking insects in the goddamn fucking swamp, in the goddamn fucking sun, in the goddamn fucking rain".
In the Duckman episode "Forbidden Fruit", Fluffy and Uranus cut loose with one of these after Duckman finally manages to drive them over the edge by staying at/destroying their house.
Cher does this (and says a lot of, um, other stuff) to Jay Sherman in an episode of The Critic.
The Powerpuff Girls episode "Curses" has the girls overhearing a profanity uttered by the Professor. Not knowing it was a vulgarity, the girls think it's neat and spend the episode repeating it, much to the shock of the citizens and their teacher.
Lana does this in Archer when she sticks her hand in dry ice, thinking that it was regular ice.
Happens again in "Heart of Archness, Part I":
Malory: Sterling's been missing for three months and you idiots have nothing! Gillette: Well first of all, name calling isn't gonna get us — Malory: [Eight straight seconds of the censor beep] Gillette: anywhere.
The Hungarian dub of King of the Hill took a quite realistic approach with its dialog, in that the characters talk like real-life people would, with all the swear words you might expect. Episodes that don't have at least half a dozen uncensored, clearly audible cuss words are rare. Hank's voice actor especially likes to stress his "fuck"s, "dick"s and "cunt"s, while there is usually a "fuck" hidden in just about everything Boomhauer says.
Used occasionally on Robot Chicken. For instance, when Dick Cheney steals Tony Stark's original Iron Man prototype, he adopts "go fuck yourself" as a catch phrase.
Palpatine in the Star Wars specials seems to adopt this. Then again, seeing how the same specials also depict Palpatine as a potty mouth, it isn't surprising.
Attempted by Phineas of Phineas and Ferb, though with his innocence it doesn't quite go as planned;
Phineas: We'll build the best dang carwash in the whole dang world, dangit! I can't really pull that off, can I? Ferb: You're not very street.
Family Guy rarely has major swearing but after the series was revived, there has been a good amount of cursing by everyone in the show and just as much in the Star Wars spoofs, especially the uncut DVD version.
A great example of a Cluster F-Bomb in a cutaway gag is where Dick Cheney is a door greeter at Walmart. His greeting to every person to walk in the door is a melancholic "Go fuck yourself."
"GET OUT OF THE FUCKING CAR!!! GET OUT OF THE FUCKING CAR RIGHT NOW MAN!!!"
In the movie special episode "Stewie Griffin: The Untold Story", future Chris' wife launches F bomb after F bomb, such as "Stop fucking apologizing!" and "That was some fucking good dinner, Mrs. Griffin!" After she insults Stewie, he drops an F bomb of his own against her.
Family Guy managed to get one on Adult Swim using the French word for seal.
"The Blind Side" has one of the most iconic uses of this trope in animation, specifically the Running Gag with Peter falling down the new stairs throughout the episode, swearing up a storm each time. The gag gets funnier every single time, particularly the one with the sandpaper. It's so funny that you may not be able to decide whether it's funnier censored or uncensored.
"The First No L" has Lois dragging a bin full of Christmas decorations down the stairs, repeatedly swearing in frustration as she gets the decorations down each step.
Fred Jones of Scooby-Doo fame pulled this off during a Cartoon Network Scooby-Doo bumper, going on a curse-filled rant about his ascot, when people asked, why the scarf? The rest of his friends are deeply offended by Freddy's Cluster F-Bomb.
The Powerpuff Girls (2016): Bubbles lets a (censored) one loose to Eddie in "In The Garden of Good and Eddie" after she's had enough with Eddie's obnoxious behavior.
American Dad!: In "You Debt Your Life" Barry gets put in charge of the school announcements. After several seconds of calmly preparing himself, he suddenly explodes:
Barry: You fucking fuckers are gonna do what I say or I will put my goddamn foot so far up your assholes you will rue the day you crawled out of your mother's twat!