This happens to Finn a lot, but by far his biggest example was in "The New Frontier". Nearly losing your best friend/only relative to a You Can't Fight Fate type of suicide? Not the best thing to happen to you. He also has another one in "Too Young" when Princess Bubblegum just broke up with him, and he goes through a Heroic BSOD when she pushes him further away in "Incendium".
Lots of recent episodes seem to be this trope on laser guidance. Finn tries to get one tiny thing done and the entire world gangs up on him. See "Blood under the skin", "Another Way", etc.
As it turns out, the Ice King is a pre-broken Cutie. He was a normal human studying to be an antiquarian until he stumbled upon the crown. He only put it on because he thought it would make his fiance laugh, but it caused some unexplained event that drove his fiance to leave him before gradually driving him insane.
The 8 children of All Grown Up! play a role in this trope. As babies in Rugrats, Tommy, Chuckie, Phil, Lil, and Kimi (excluding Dil, due to being a few months too young at the time for character development) had no serious worries (aside from Angelica and other episodic misunderstandings) compared to their 10-year pre-teen future-selves. In All Grown Up, the children deal with various life difficulties as they attend school. Occasionally, the problems they face would delve into heavier issues, which would put them at each other's throats, like a loose spoof of Degrassi, making their toddler years seem like bliss.
Some example would include Tommy and Chuckie's friendship being strained in "Fear of Falling" and "TP + KF", Phil & Lil having a less-than-inseparable bond in "Coup Deville" and "Separate But Equal", and Chuckie and Kimi's sibling bond being strained in "Memoirs of a Finster" and "Petition This".
Happens to Prince Zuko prior to the show's timeline. Flashbacks of younger Zuko portray an idealistic young man with a thirst for knowledge and experience to help him learn to be a good leader and a genuine concern for the welfare of his nation's citizens. True, he's arrogant and brash, but hey he's a teenage boy and Royalty. His naivety results in a serious disagreement with his father that leads to his scarring and banishment. By the time the other characters encounter him he's bitter, angry and obsessed with doing whatever it takes to regain his father's approval. It doesn't help that actions stemming from his inherent "good" side often backfire. Spare Zhao's life? Zhao tries to kill him- several times. Help the little boy bullied by thuggish soldiers? Whole village turns on him because he has to resort to Firebending to do so. Share a moment of introspection with a fellow traveler? Said traveler tries to recruit him, then stalks and attacks him. Offer a bit of compassion to a fellow prisoner? Seems to work, as Katara offers to heal him, then Aang shows up, and Katara runs to him. Well, No Good Deed Goes Unpunished.
Aang himself starts off as this rather goofy, optimistic kid. Then learns that his own people have been killed off, everyone he ever knew it gone, that he's capable of pretty horrible destruction and might need to kill people.
"Appa's Lost Days" does this to Appa. Kidnapped by Sandbenders, sold to a circus, beaten, sleep-deprived, forced to abandon friends in need, and captured again. This flying bison needs a freaking break!
Katara herself suffered this very early in her life, before the series even started when her mother was executed in cold-blood.
Jet counts. He's probably one of the last characters on the show anyone would describe as a "cutie" (Well, unless you're using a certain connotation of the word), but a flashback scene shows a little 8-year-old Jet sobbing while watching his village burn down... which is what turns him into the thug he is when the Gaang meets him.
The Joker did this in Batman Beyond: Return of the Joker where during Bruce's time he kidnaps Tim Drake and tortures/MindRapes him into giving up Batman's secrets (including Secret Identity) as well as making him into a miniature version of The Joker known as J.J (Joker Jr.) to fit into a sick excuse of a family unit with Harley Quinn and him. This is shown as enough to convince Batman to try and kill Joker, (meaning the Joker finally broke Batman, too) which he fails to do... but is saved by the still-broken Tim killing the Joker after Joker tries to get him to kill the subdued Batman. This only further adds to his trauma. Although he does get better, Tim is forever traumatized and never again becomes Robin in the DCAU.
Shifty Dingo from Blinky Bill takes a lot of crap. In the wedding picnic episode, he gets bitten on the leg by Marcia, cries his eyes out, fails at dance steps, cries his eyes out again, breaks his leg while practicing dance steps and his own mother won't let his friends give him flowers to cheer him up. Ouch. In another episode, he saves Marcia with CPR and her reaction? "Yuck kissed by a dingo!" and then shepunches him in the face. He frequently gets picked on in multiple episodes and Nutsy is one of the only characters to stand up for him.
Max from Capitol Critters is a sweet little midwestern fieldmouse from Nebraska with Puppy-Dog Eyes. In the first episode, he watches his own family get gassed to death. In later episodes, he nearly dies from smoke inhalation and a forced drug overdose from a gang member and in another episode, he breaks down in tears when he thinks he accidentally killed a cat, falls in love with a girl who has to move back to Japan and in general plays to Only Sane Man to a bunch of jerkasses. Poor Max...
Aelita from Code Lyoko gets this treatment over the course of the series. She never actually breaks (although she gets quite close to suicide in the Season 2 finale), but dang, the poor girl's been to hell and back. And it doesn't get much better in the end, when XANA is finally defeated... at the cost of her father's life.
In an episode of Dexter's Laboratory, DeeDee breaks when she loses her teddy bear, Mr. Fuzzums. Throughout the episode, she is catatonic and only speaks by muttering, "Fuzzum uzzum, uzzum, uzzum fuzzum," etc. She is fixed by the end of the episode.
This happens to the title character of Doug during the Nickelodeon Christmas special. After his dog, Porkchop, ends up biting Beebe Bluff while she and the other main kids were playing hockey (he was actually trying to save her from the thin ice) and she gets badly injured, poor Porkchop ends up having to be taken to the pound and has to be put on trial. The day before the trial, Doug remembers about how he got Porkchop for Christmas when he was a year old, and how the previous Christmas, he got him his journal. Then, because of how Porkchop is being treated by everyone in town, he imagines standing at Porkchop's grave, and begins to cry. He really needed a hug in this episode.
Double D from Ed, Edd n Eddy has had 2 major ones near the end of the series. The first one happens in 'A Fistful of Ed' and the finale. In the former episode, the poor guy has accident after accident, resulting in many of the kids getting injured very badly. This leads to him getting exiled out of society more than he already was, and boy is it hard on him. At least it ended well for him. In the movie though, he ends up a fugitive along with the rest of the Eds, gets dragged along a wild goose chase, and gets treated like how he was for most of the series. But it all comes to a head when he's pranked by Ed and Eddy into thinking that they sunk in quicksand. After that, he verbally and physically goes hog wild on Eddy:
Eddy: "Hey! (He and Ed follow Edd) Where ya goin? You're headed back into the swamp! (reaches for Edd's shoulder) My bro don't live–"
Edd: (slapping his hand away) "Don't you dare touch me!" (begins to let it all out) "A sap? Well excuse my sincerity, but thinking I had lost the only two people I have left in this world–"
Eddy: (smiling, sure Edd's putting on an act) "And?"
Edd: (angrier) "It's surprising, because your stubborn, inane desire to scam, sandbag, and swindle is what put us here in the first place!"
Ed: (indignant) "I helped too!" Edd turns to Ed angrily before then turning back to Eddy.
Edd: "You and your nefarious scams!"
Eddy: (Realizes the seriousness of the situation, and becomes angry as well) "Like you were picking daisies! You built the stupid thing!"
Edd: "If you had paid attention to what I said and not pushed the red button–" (a fight ensues)
Ed: "Stop! I demand you tickle each other right now!"
Edd and Eddy: "Stay out of it, Ed!"
Ed: "The evil dark side has consumed them both! Trouble! Bad! Pain!"
Edd: "I've had enough!" (kicks Eddy off.) "I'm returning home!"
Ed: "But we can't go home, Double D!"
Edd: "I'd rather face my consequences, Ed, than wander aimlessly with a so-called friend!"
After that, Eddy breaks down in tears and shows massive contempt for his actions. This wins him back he and Edd's friendship, and the reunited trio continue their journey from there.
Jimmy has it even worse. If you push his buttons and he doesn't bawl his eyes out, he will get either violent or downright malicious.
Family Guy usually plays with this as most of the characters go through some of the most horrible incidents that someone can go through. But it's played straight with Lois during the Christmas Episode in the earlier seasons. All the presents given to another family? Hey, another family benefits from the charity. House burn down? At least everyones safe. Your turkey is ruined? We can work something out. Out of paper-towels? Oh, snap.
When Bloo became a celebrity and was ignoring him (it was actually because his manager was nasty). (He gets better).
2-D of the Gorillaz gets pretty thoroughly broken over the course of the story. It all starts when he gets run over and knocked into a coma at age 19... which is how he met his 'friend' Murdoc. From then on he is run over again, has his front teeth bashed out, beaten silly countless times, kidnapped, held captive against his will, harvested for organs and mentally tortured. Granted, 2-D is by no means a saint, but he was always pretty harmless. At this point, it's nigh-impossible not to feel kind of sorry for him.
Gravity Falls: In "Boss Mabel", when the Mystery Shack employees take advantage of Mabel's generosity one time too many, she completely snaps, and begins angrily barking orders like her uncle.
Flippy from Happy Tree Friends starts out as a cute, friendly, fun loving bear but whenever he sees or hears something that reminds him of the War he transforms into a cruel, murderous, psychopath.
Dib from Invader Zim, through YMMV. If you count him to be cute and The Woobie. During the course of the show, he gets laughed at, gets pummeled by his sister (numerous times), gets threatened to be eaten by mechanical stuffed animals, has a water balloon CONTAINING ALL THE WATER ON PLANET EARTH dropped on his head, is held over the city cesspool for a day, gets thrown into a slowly expanding explosion, gets put into a Lotus-Eater Machine and has a wonderful life, until he realizes that it was all a dream, gets shot with a gigantic laser gun (albeit using muffins as ammo,) gets laughed at again, gets pummeled by a monkey, and his LANDING-PAD-SIZED MONSTER OF A HEAD THAT IS ALSO DISTURBINGLY LARGE? He cracks appropriately.
Drakken, Monkey Fist and Killigan nearly do this to Kim Possible. When they go after Ron however, she breaks them.
Drakken tries this again in So The Drama, by creating a "perfect boyfriend" for Kim and having him betray her when she is most vulnerable. When she realizes the truth, she nearly gives up, saying, "Drakken won. I should have stuck to babysitting." Ron pulled her out of her funk, and in the process instigated their Relationship Upgrade.
Toki Wartooth from Metalocalypse. Man, season 2 broke that cutie. Yet, being an Adult Swim show, this is all somehow played for (very dark) laughs.
Orel himself, during the infamous "Nature" two parter. In the span of 2 episode, thanks to his drunk father shooting him in the leg, blaming Orel for it, and passing out drunk for two days the usually chipper Orel is broken something fierce, and he's never quite the same from then on. Interestingly as the third season goes on it seems like this is Clay's whole motivation. To make up for his own shittiness he tries to prove that Orel is not really as pure, good, and innocent as he seems and that his religious beliefs are built on sand. When Orel proves him wrong it drives Clay crazy.
Pinkie Pie from My Little Pony: Friendship Is Magic in "Party of One" reverts to her depressed, straight-haired state previously seen in "Cutie Mark Chronicles" when she thinks her friends don't like her or her parties anymore.
All of the main characters have a turn at breaking; usually, it happens because the aspect of their lives symbolized by the markings on their flanks has been called into question. This is the root cause of so many pony breakdowns that the fandom has dubbed it "Cutie Mark Failure Insanity Syndrome".
This is made especially prominent in "The Best Night Ever." All the ponies are broken to a certain extent, but none more than Fluttershy, who is of course the super-incredibly-shy one. When the animals at the gardens at the Royal Palace subvert her special talent of caring for wildlife by running away from her, she snaps, chasing them, diabolically concocting traps (complete with Twitchy Eye, Evil Laughter, and Dramatic Thunder), and screaming at them to love her.
Discord loves doing this (though he admittedly slides between this and Corrupt the Cutie). Twilight is the only one to escape his , and the fact her friends are brainwashed it's likely he got to her too. Fluttershy manages to partly avoid it by virtue of being aware and accepting of her faults, but he still brainwashes her anyway.
Even though Twilight isn't brainwashed directly, she still gets hit with this. Discord reunites her with her friends after he's finished breaking them. The result is Twilight being treated like dirt by her beloved True Companions and having no idea what's happening to them. By the time the corrupted Fluttershy verbally assaults her, the poor girl has been broken as well. It gets so bad in the second episode that she turns gray without brainwashing.
Applejack gets this treatment two episodes in a row. In "The Last Round-up", her inability to win a single blue ribbon or earn any prize money for Ponyville breaks her so hard that she can't face returning to Ponyville since she feels she has let everyone down. In "The Super Speedy Cider Squeezy 6000", she is understandably driven to tears by the apparent loss of her and her family's home and vocation.
Pinkie (again; she seems to get a lot of this) and Rarity are driven to tears by numerous insults from Fluttershy, when the pegasus tries to act more assertive in "Putting Your Hoof Down." Included among these is Fluttershy calling Pinkie "simple," calling Rarity "petty," and saying that the pursuits to which both ponies have dedicated their lives to are useless (coupled with a Hold Your Hippogriffs-disguised Precision F-Strike, no less). Note that neither of them did anything to deserve this treatment — they only tried to help Fluttershy and expressed concern about her recent behavior.
Fluttershy gets this hard in Hurricane Fluttershy. In fact, it happens three times! First is when Rainbow Dash trying to get her to join in making the tornado brings up a pretty brutal bullying incident from her foalhood. Second is when some ponies laugh at her wing speed test, sending her running off as she cries her eyes out. And then, after she gives it her all to improve her performance by training extensively, she takes the test again only to find out that the improvement she's made isn't nearly enough and once more runs off in tears. Poor thing...
In "A Canterlot Wedding," the characters all attend the wedding of Princess Cadance and Twilight's older brother, Shining Armor. Sounds completely lighthearted, right? Not after Twilight's hostile confrontation against Cadance at the wedding rehearsal causes Shining Armor to strip her of her "best mare" position and rescind her invitation to the wedding altogether, after which all of her friends and her idol, Princess Celestia, follow his lead and coldly turn on her (the point is then driven further home with a Dark Reprise sung by Twilight lamenting the loss of both her sister-to-be and her brother). Suddenly, Cadance reappears by Twilight's side, and for a moment it looks like all will be forgiven - and then Cadance claims she'llmake Twilight sorry, ends Part 1 of the episode by imprisoning Twilight with dark magic, and starts off Part 2 by taunting Twilight with the fact that no one will ever hear or come looking for her.
Cadence herself goes through a phase of this in Part 2, when she believes that she'll never make it to her husband-to-be in time. Twilight snaps her out of it, though.
Pinkie again in "Too Many Pinkie Pies". She has a breakdown when the clones she created to spend time with her friends cause trouble for them with their fun-seeking antics. Then she has to endure a test to prove that she is the real one with her very existence on the line.
The CMC in "One Bad Apple", thanks to bullying by Babs Seed. Unlike Diamond Tiara and Silver Spoon, Babs' bullying is much more serious and brutal. Justified, as this episode was intended to address the serious issue of bullying in Real Life.
Sweetie Belle: Why do I feel like crying?note And she does, when Babs takes the CMC's clubhouse from them.
Pinkie yet again (Geez, Hasbro) in "Wonderbolts Academy" is driven to a sleepless near-insanity that can't leave the mailbox when she goes a few days without getting a letter from Rainbow Dash and thinks she's forgotten about her.
The Mane Six in "Magical Mystery Cure". Twilight inadvertently causes her friends' cutie marks - and destinies - to be switched, and her friends are unable to cope with the jobs they now believe they were always meant to be doing. Seeing her friends break down leads Twilight to tears herself, until Spike helps her remember just how important her friends are to her, giving her the spark of inspiration she needed to fix the problem.
On "Phineas and Ferb Get Busted", Phineas and Ferb's latest invention actually destroys the house and they are caught by their mom. Even though they believed they had permission, they're shipped off to reform school, where they are tortured and stripped of their identities and creativity, afraid to even touch on of their tools. It's all a dream, but still a pretty horrid What If? episode.
On "Summer Belongs To You", the crew is stranded on an island with no resources, and Phineas has a nervous breakdown because he can't build anything to help them.
Averted in The Powerpuff Girls. Him seems bent on destroying the Powerpuffs (especially Bubbles) mentally and came close a few times (like in "Speed Demon", "Power Noia", and "All Chalked Up"). However he failed every time.
Though, played semi-straight in the episode "Bubblevicious". Bubbles essentially induces this on herself, trying to become as strong as her sisters. She loses her sweet act and becomes rather brütal (Read: bitchy). This culminates with Bubbles taking it Up to Eleven after Mojo Jojo tries to torture her and break her even further. Bubbles wouldn't have any of that shit. Luckily, though, after probably deadening a majority of Mojo's nerve cells, her sisters come and snap her out of it quite quickly.
The animated Punky Brewster episode "Punky The Heiress" has her aunt and uncle playing her like a violin in order to embezzle an inheritance. They dress Punky up to look like the heiress of a missing tycoon's fortune and make her think she's going to be reunited with her missing mother, until Glomer overhears the plan and breaks it to her. It understandably devastates her.
The Recess finale "Lost Leader" does this to T.J.. After one of his plans goes wrong and injures Gus in the process, he has a Heroic BSOD and absolutely refuses to lead the gang with their plans.
The unproduced Renand Stimpy episode "Life Sucks" was going to be a huge one for Stimpy; fans have guessed it was a prelude to Ren Seeks Help, where poor Stimpy is finally broken.
In "Son Of Stimpy", Stimpy (a generally happy character) tries to find his flying fart but when he fails to find him for a while, he then becomes depressed to the point where he goes out into the cold winter looking for him. It's one of the saddest episodes in the series. Fortunatley, he eventually meets him again when the flying fart arrives home.
Scooby-Doo! Mystery Incorporated breaks all four at once in the season finale. After Mayor Jones is revealed to not only have been the Freak Of Crystal Cove and kidnapped Freddy as an infant from his real parents to raise, but now Freddy has dissolved the team to look for his parents. Meanwhile, Shaggy's parents are shipping him to military school, and Velma is on the outs with everyone for keeping Angel Dynamite's identity a secret from them. Daphne is absolutely devastated as Fred had proposed marriage to her in episode 24, but now that's off as Fred seeks to discover who he really is.
Played straight with Ralph when he takes Lisa out to Krusty's anniversary special, only for her to dump him on live TV.
Bart (replaying a video of the event): Watch this, Lis. You can actually pinpoint the second his heart breaks in half.
One of the usually playful and rambunctious Nahasapeemapetilon Octuplets, Anoop, becomes this in the alternate future of the episode "Future-Drama". When Bart works part-time at the Kwik-E-Mart, he (along with the other Octuplets) is very bossy and sadistic to him, going as far as to kick him in the head (while wearing a hover pack).
Anoop: You missed a spot! (spits on the floor) Do it again!
Bart: Yes, Mr. Gheet...
Anoop: I'm Anoop, you racist cracker! (kicks Bart in the head)
Perhaps the most memorable example is "Hurricane Neddy". Ned Flanders loses his home to a hurricane, made worse by the fact that he followed all precautions and was the only one to end up homeless. He then lost his business to post-disaster looting. Just when things seemed hopeless, his neighbors rebuild his house... but do such a poor job at it that it collapses shortly thereafter. Then when his glasses break, the normally calm and saintly Flanders finally snaps, tells off everyone in town, and drives himself to the psychiatric ward.
Butters from South Park snapping and becoming Professor Chaos. He seems to revert back rather easily, though.
It happens again when he becomes a "vampire" (actually just a fad of pretending to be a vampire induced by the new Twilight movie, but he thinks it's real)
Kyle gets this as well, most notably in Cartmanland. It's one thing into being pushed into denouncing the existence of a God (or in this case a righteous God). It's another to be pushed to the point of giving up on life due to Cartman's constant Karma Houdini instances. It takes one major case of divine intervention to rectify.
In season 15, Kyle isn't the only one who gets broken, but Stan and Cartman, too. Stan spends 2 episodes in a state of cynicism that worsens after his parents temporarily divorce again, and Cartman breaks when he destroys all of his stuffed animals in order to be more mature.
Terra from the animated Teen Titans started out cracked, then met Slade, who did his best to finish breaking her.
Some villains attempt to do this a few other Titans, but they usually recover or defeat the villain tormenting them.
Transformers Animated: Sari in Season 2. First her dad goes missing, then her dad's company gets taken out of her control by Porter C. Powell who reveals with the subtlety of a brick that she doesn't exist in any form of legal documentation. If it weren't for the Autobots helping her cope over all of this, Sari could very easily have snapped upon the revelation that she was part Cybertronian instead of taking a level in badass.
Wakfu, episode 19: Sadlygrove, possessed by the demon of his sword, proceed to crush both forearm and bow of Love Interest Evangelyne, who has only just begun to reciprocate his feelings, in one grasp. The tears of physical and emotional pain she show afterwards are enough to cause a My God, What Have I Done? moment in Sadlygrove, almost making him another broken cutie.
Nerissa tried to do this to Hay Lin in the second-season W.I.T.C.H. episode "T is for Trauma", first by exploiting the fact that Hay Lin's grandmother Yan Lin had just betrayed her (though it was actually a brainwashed clone), secondly by using her good looks (in her youthful Uncanny Valley Girl form) to seduce Hay Lin's boyfriend Eric away (though again, she had to brainwash him), and thirdly, by trying to make Hay Lin feel insecure about her new braces. She finishes all this up by trying to kill Eric, but Hay Lin ends up pulling herself together and saving him.
This is what the first arc of the X-Men cartoon was trying to do to Jubilee. The Unspoken Backstory that her parents had been killed (by assassins looking for the Lees down the street and got lost) and she was in a foster home, then when she'd finally come to terms with THAT, they register her with a front organization for Project Wideawake. So the Sentinels come, after she runs away. Oh, but that doesn't stop the metal monsters from killing her step-parents. It may not get worse, but it doesn't get better quickly.
The Young Justice episode "Failsafe" breaks Miss Martian, after she loses control of her powers and accidentally pulls a Holodeck Malfunction on the team during a training exercise, rewriting their memories to make them believe the simulation was real and leaving them all in comas when they "died." She collapses in tears at the end of the episode when she learns what happened.
The Holodeck Malfunction a pretty good job of breaking Robin, too. It's not really touched upon until the following episode, but the burden of sending his friends to their deaths took its toll on him, and made him realize that he didn't want to become the Batman.
In "Misplaced" it's Zatanna's turn to be broken when her father takes her place as Nabu's host (effectively killing him). One of the last scenes of the episode is Zatanna sitting alone in her new room at Young Justice headquarters crying her heart out.
Miss Martian, again, starting about 1/3 of the way through "Depths" and several episodes afterwards where she commits Mind Rape against Aqualad, discovering that he was The Mole all along, but destroying his mind in the process.