Villainous Breakdown/Fan Works

In the All Things Probable story, A Friend In Darkness, Monkey Fist, who was usually the most calm-minded and suave villain in the series, suffers from one of these in the final battle of the story after being humiliated, reducing him to raging and shrieking like an actual monkey while unleashing the dark power he had been cursed by. The irony is, his breakdown wasn't caused by Ron Stoppable, his actual Arch Enemy and the one more likely to drive him into one.
In the The Familiar of Zero/Fate/stay night crossover The Hill Of Swords the villainess Sheffield starts out as a Smug Super supremely confident mage that swiftly devolves into a raving lunatic as Shirou outmatches her in each of their encounters. During their final encounter in chapter 22 she spends quite a bit of it just shrieking "DIE!" as Shirou refuses to do just that. The breakdown is so bad that she falls for one of the oldest tricks in the book: the old "your shoelace is untied" gag.
In the Law & Order: Special Victims Unit fanfic Girls' School, Lucy Horowitz, a girl accused of holding down another girl as the other girl was raped, has one after learning that the rapist was caught, thus denying her a bargaining chip for a reduced sentence.
In The Legend of Spyro fanfic A Dark Beginning, Dredd, the commanding Ape on the Tall Plains, has one of these after he discovers Kane escaped, going from Faux Affably Evil to screaming his death threats and his You Have Failed Me... trait surfacing. After he falls for Spyro and company's plan to free and arm his captives, resulting in his entire group to be wiped out, he's left stunned at what happened before getting enraged and going into a Last Villain Stand against Kane that leads to his demise.
The Big Bad in The Man With No Name has a mental battle with the Doctor. After the villain wins, the Doctor reveals that's exactly what he wanted him to do, as his mind is now trapped. Breakdown ensues.
Loneliness from the Pony POV Series loses her cool a bit every time Twilight manages to fend off her mind games, but snaps completely once Twilight actually manages to break through to Trixie. Loneliness goes One-Winged Angel and drops her facade of "love" towards Trixie, breaking her leg and outright trying to murder Twilight rather than let Trixie escape her clutches.
- Discord has two in "Origins". The first is when Mimic reveals to him that the bridge between Ponyland and Earth has been destroyed, thus protecting humanity from him. Discord is rendered speechless for a few minutes and left so beside himself with anger as to forget he's an omnipotent Reality Warper long enough for Mimic to perform her now famous Dying Moment of Awesome. The second comes when Shady, his Dragon and earthly mother whose love for him he's manipulated for 1000 years, betrays him, allowing Celestia and Luna to defeat him.
Discord had a hysterical breakdown in Progress, when Luna turned him to stone in the dream world. He went from psychotic fury to frantically pleading for mercy in the space of a few seconds.
Several in With Strings Attached:
- Kerrun as she realizes that the four aren't on her side after all; and, later, when she goes off the deep end completely and declares that every skahs in Ehndris is actually an Idri.
- Jeft has two:
  - When the Hunter makes friends with the four instead of fighting them, Jeft is so pissed at this subversion of his favorite gaming character that he sics square miles of undead on them as payback. He freaks out completely when the five manage to destroy the Heart of Evil powering the whole show.
  - A few hours later, when the Hunter agrees to ditch his BFS in order to return to C'hou with the four, the still-simmering Jeft goes crazy with anger and turns the sword back into the demon it always was in an attempt to kill the four and regain control of the Hunter.
Vaticus in The Tainted Grimoire had a brief one before being defeated. He became a Graceful Loser after being defeated.
Razor in Ace Combat: The Equestrian War. Due to Garuda team performing a Big Damn Heroes and preventing the bombing of Stalliongrad's Eastern Sector. When he tries to do it himself later, Mobius defeats him.
In Project Gethinator, the Big Bad, Admiral Daro'Xen, who is Yandere in a big way for Commander Shepard, loses it quite spectacularly after Shepard decisively turns down her advances and calls her on her crazy scheme and her obsession with him. Her breakdown is of literally star-system-shattering proportions -- she takes the same mineral scanner that Prazza, Tali's idiot crewman from Inglorious Boshtets, accidentally used to make a star go supernova and uses it on the main star of the Eta Carinae system to make the thing go hyper-nova, making sure to have the Normandy's drive core disabled so Shepard, Tali and the crew cannot escape. When the crew does manage to escape Just in Time (via Shepard's quick thinking and Legion's advanced skills getting everyone out of there alive), Xen proceeds to lose it even further.
Loki, the Big Bad of My Little Avengers (a Fusion Fic of My Little Pony: Friendship Is Magic and Marvel Comics) loses it during the Final Battle when Big Macintosh not only regains Thor's powers, but reveals that he isn't Loki's Worthy Opponent brother reborn -- as everyone had assumed -- but just a "mere" earth pony with his powers and some of his memories. Likewise, his Dark Avengers each have small scale ones of their own during their own fights with the other Avengers -- Ghost Flyer has the "This Cannot Be!"-panic variety when Captain Equestria breaks through his Penance Stare through sheer willpower, while Iron Monger and Red Skull both go into blind rages when Firebird and Iron Pony turn their own Hannibal Lectures back on them.
Queen of All Oni: Lung starts cracking when it becomes evident that his plan to break Jade to his will is failing, and then he breaks completely when her minions show up to save her.
- Drago eventually has one due to the repeated failures of his attempts to gain power in the past. He ultimately snaps and rants that rather than doing things strategically, he's just going to smash everyone and everything in sight and see what effect that has on the timeline. Fortunately, he's banished back to the future before he has a chance to.
Freeza gets it bad in Dragonball Z Abridged during his fight with Goku, due to his exposure to Goku's remarkable stupidity.
Ponies Make War has a couple. First, Nihilus -- who wasn't all that sane to begin with -- completely loses her shit when Rainbow Dash not only breaks free of her mind control, but she learns that she hasn't corrupted the Elements of Harmony, as she thought. Then, near the end of the story, Empyrean totally falls apart when the Mane Six break into his throne room to confront him, and fires off the magical equivalent of a Wave Motion Gun to try and fry them only for the Elements to be used to strip his powers instead.
In Fever Dreams when L screws up his plan to get them back together Light very calmly goes up to his room, collapses into bed, and screams into his pillow.

Rem: Light Yagami, I did not realize you were capable of having feelings.

Inner Demons: Twilight Sparkle stopped being sane the moment she was consumed by her Queen persona, but even by that standard she really flips her shit during the Battle of Fillydelphia when she realizes that her beloved brother is choosing to stand against her with the protagonists. She starts ranting and screaming that she'll kill all the heroes, Shining Armor included, and is only stopped from carrying out an execution on Cadence by the other heroes arriving in time. Interestingly, they also somewhat accidentally calm her down from the breakdown when they then confront her over Trixie killing Rarity on her orders.