Allfather Starr towards the end of Preacher. The abuses and mutilations he suffers over the series in pursuit of Genesis take a heavy toll, to the point where the final story arc has him pointing a gun at the mirror and saying "Doom cock" over and over again and gassing his advisors when they say they're abandoning the pursuit of Jesse Custer.
Venom (Eddie Brock), in an issue of Spider-Man, suffers a villainous breakdown after he recieves a touch of death from another villain. Eddie Brock is unharmed as his body is protected by the symbiote but the symbiote itself seemingly dies as it melts into a lifeless, motionless, puddle. Brock, who up to this point has lost everything and now the only friend he had is dead, breaks down and cries for his fallen partner. Even Spider-Man, who has been stalked and tormented relentlessly by Venom, can't help but to feel sorry for Brock.
Kingpin in Ultimate Spider-Man; after being completely in control through the entire series, manipulating everyone and getting away with murdering someone with his bare hands and taping it, his schemes are thwarted by Daredevil holding the only thing he cares about, his comatose wife, hostage. As he's on the way to a flight to leave the country, he has a Villainous Breakdown during which he orders his henchmen to bomb a high school while it's in session.
The further bitter irony here is that the ordered bomb is intended to kill Spider-Man... when it was Spider-Man who talked Daredevil down from killing Kingpin's wife out of sheer desperation, thus saving her life.
Kingpin's first story arc in Ultimate Spider-Man also played this trope for laughs. After spending several issues as a smug, collected crime boss, he's reduced to a screaming, enraged fit when Spider-Man attacks him with a barrage of "You're so fat" jokes.
Riddler has a rather nice one in Batman: Gotham Adventures #11. After escaping Arkham he decides that the best way to beat his urge to commit crimes and leave riddles (thus guaranteeing that Batman will eventually catch up to him) is to solve crimes himself and leave Batman riddles pertaining to them. After catching several wanted criminals thanks to the Riddler's hints (which you'd think would be convenient enough that he wouldn't be in such a hurry to end it), Batman figures out that all the clues contain part of a hidden riddle which leads him right to Riddler. Upon learning that his psychosis is so deep that he left Batman a clue without even realizing it, Riddler freaks out, screaming about how impossible it is. Then he comes to his senses:
"You don't understand... I really didn't want to leave you any clues. I really planned never to go back to Arkham Asylum. But I left you a clue anyway. So I... I have to go back there. Because I might need help. I... I might actually be crazy."
In Superman/Batman, when President Lex Luthor's scheme to smash a Kryptonite asteroid into the Earth fails, Luthor (who was the U.S. President at the time) uses a variant combination of the "super-steroid" Venom (a chemical associated with the Batman villain Bane), liquid synthetic Kryptonite, and an Apokoliptian battlesuit to go on a violent rampage. This, unsurprisingly, gets him impeached.
He gets a worse one in The Black Ring. After traveling across the planet and in space in an attempt to regain something like the Orange Lantern Power Ring, Luthor gains the powers of a creature from the Phantom Zone and proceeds to use it to torture Superman. Once he finds out that Superman is Clark Kent, though, he loses it. It gets worse as he manages to make the universe perfect for a few minutes. He swiftly learns, however, that in order to cement this power, he must not use this power for violence... including against Superman, who is right in front of him. Supes, being Supes, begs him to let go of their old grudges in the name of unending peace. Lex's response? "YOU DARE TO LECTURE ME?" And thus was universal bliss ended. And tucked away in Arkham, The Joker laughs away at what Luthor had done.
A classic Silver Age "imaginary story" Has Luthor finally managing to kill Superman and mobsters throw him a celebration party as he gloats on how he did it. When a red and blue caped figure bursts in, a terrified Luthor worries Superman has come back to haunt him. It turns out to be Supergirl (whose existence was unknown to the world at the time) who arrests Luthor and takes him to the bottle city of Kandor. Luthor spends his televised murder trial smug that he'll find a way out of this. When he's found guilty, Luthor offers to restore Kandor to its regular size in exchange for his freedom, confident they'll agree. Instead, the judge declares "we Kandorians do not make deals with murderers!" Unable to accept losing like this, Luthor begs for mercy but it's too late as he's sent to spend eternity in the Phantom Zone.
The second Sabbac over in DC Comics is constantly just on the edge of this. Most of the time he's calm, cocky and sarcastic. But when he doesn't get what he wants, when things don't go his way, he loses it entirely, screaming and ranting as he kills friend and foe alike. Imagine a greedy ten year old with the power to destroy a small nation and you've got Sabbac.
In Archie's Sonic the Hedgehog comic, Dr. Eggman began to suffer mentally as a result of the constant defeat at Sonic's hands. This finally came forward after his latest defeat, which turned him into a babbling madman. He spent the next few issues in a padded cell, wearing a straitjacket.
If you read the issue, its art suggests that Snively is calling Sonic out for putting Dr. Robotnik, or Eggman if you prefer, in that condition to begin with.
As well, despite snapping himself out of it, Dr. Eggman has yet to really recover from the moment, going so far as to leave the Freedom Fighters to grieve at Antoine's seeming death instead of wiping them out right then and there. It pisses Snively off so much he pulls a Screw This, I'm Outta Here! and decides to handle things his way again. However, it's hinted that this is not Eggman not recovering, but his subordinates not realizing that using the same tactics over and over is not a good idea.
Fleetway's Sonic the Comic Dr. Robotnik did it about 8-9 years earlier, for much the same reasons. During the Sonic Adventure storyline, he cracks and goes from wanting to conquer the world to just flat-out destroying it because he sees it as the only way to rid himself of Sonic.
Scourge also qualifies. After being betrayed by The Supression Squad and ganged up on by everybody, he retreats to his throne and goes super from the Anarchy Beryls he's stashed there. Then as he blasted everyone off of him and hunts down Sonic, he declares that he's going to spin dash both Mobius and Moebius in half, simply because he can.
This was the premise of the Thunderbolts "Caged Angels" arc by Warren Ellis. A group of incarcerated telepaths drive each member of the alreadyunstable team over the edge (Except for Bullseye, who can't get any crazier.) The best one is Norman Osborn, starts walking around naked ranting about what he'll do when he's president and how much fun killing people was.
It gets even better when he finally gives in and becomes the Goblin again, and all it took was the mere mention of Spider.
Swordsman: ...mother. The Green Goblin: YOU DIDN'T HAVE A MOTHER! A pig coughed, and you fell out!
Later comics in Dark Reign made it pretty clear that for all Norman's Villain with Good Publicity act, he was most of the time a hop, skip and jump away from a full psychotic breakdown. And having to maintain a good public reputation as the head of the Initiative only helped slowly push him closer to one. As was particularly cruelly lampshaded in a Breaking Speech delivered to Norman by the Molecule Man, it was a default position amongst the main players of the Marvel Universe that it wasn't not so much a question of "Will Norman crack under the strain?" as "When will Norman crack under the strain?" Several of them were waiting for his breakdown since he first took power.
It finally happened in Siege #3. Though after all the buildup it was given, and the masterful snap he had in Thunderbolts, readers found this one (a painted up face, jeans and a t-shirt under the armor, and nonsensical babbling about how his plans to save everything from the Void had been ruined) more than a little underwhelming. The part before that (where he flat-out orders Sentry to bring down the entire floating city of Asgard) was much better.
Even before Dark Reign and Thunderbolts Norman was suffering from breakdowns much more often.
Norman had a few smaller breakdowns when Loki gave him hallucinations, or when the Skrulls turned into a bunch of Spider-men to screw with him
For Osborn, the Goblin is a villainous breakdown. When the cool, collected Villain with Good Publicity and master of every gambit in the index has his plans go off the rails and he reaches the point that he starts screaming and ranting and cackling and throwing pumpkin bombs, you know it's all over. He wasn't always portrayed this way (once it was decent Osborn having the Psycho Serum take over, and he'd be defeated and forget he was the Green Goblin until next time.) Of course, the truth of the situation in Osborn's head is that Osborn on a good day is about as sane as the Joker on a bad day, and he can only act otherwise for so long. When the situation goes off the rails, this ability is strained, but putting Peter Parker aka Spiderman anywhere in his close vicinity will set Norman off regardless of whatever reputation he has to hold.
It's implied that the breakdown had been building (and was maybe already in progress) since he destroyed Kansas, it's just that Superman's arrival is what tipped it over.
Also, a large part of the reason for the breakdown was that Magog wasn't a straight villain, but a '90s Anti-Hero who tried so hard to be The Cape, and felt guilty about all the death he caused.
In Star Wars: Knights of the Old Republic Arkoh Adasca and Haazen suffer breakdowns right before meeting their deaths; Arkoh goes from Suave Businessman in complete control to a gibbering lunatic screaming at his men to murder the heroes and daring the man he abused into smiting him in an extremely nasty karmic death, and Haazen is reduced from Magnificent (if smug) bastard to a helpless wretch who can only stammer and beg Lucien not to use the McGuffin to thwart his plans and kill him in the process. Demagol also loses his coherence and stutters, and Raana completely loses her mind.
And in Star Wars: Legacy, Darth Krayt suffers a protracted one across several issues after Cade Skywalker, the one man in the galaxy who can cure his chronic illness, escapes his grasp. It gets so bad that his previously loyal Dragon, Wyyrlok, decides to kill him because he's now a liability to his own cause.
Ultimate Magneto suffers a breakdown at the climax of Ultimatum when Jean Grey shares Nick Fury's memories with him and he learns that the existence of mutants was just an accidental byproduct of a Super Soldier experiment. This information shatters Magneto's delusions of grandeur and he completely loses the will to fight.
Joe Dalton tends to go through one of these whenever someone mentions the name Lucky Luke in his presence. Usually inverted, as it tends to happen at the beginning of an episode, and as soon as he regains his calm, he devices a plan to break out of the Cardboard Prison, starting the plot.
In the Garth Ennis Dan Dare mini-series, the Mekon uses his grand finale battle with Dare to vent some long pent-up grievances:
Before that, Joker loses his temper when he uses his Reality Warper powers to torture Superman, but Supes won't go crazy or slip past the Despair Event Horizon no matter what he does.
Joker: (some torture, Superman kills himself on purpose to deny Joker's fun) What!? That's not the way I wanted this to end! I don't want the big lummox dead, I want him broken!
(brings Superman back to life, more torture) Phooey! Phooey! Phooey! To hell with this stupid broadcast! No one is following the script! I want everyone back the way they were before! Phooey! Superman wasn't breaking!
A truly heart-wrenching Legends Of The Dark Knight story titled "Going Sane" recounted how an epic fight between the Joker and Batman ended in the Dark Knight's (apparent) death. Victory freaked out the Joker so badly that his then-current personality...dissolved. Melted away, leaving a sweet, gentle man who loved old-time radio comedy and who pondered "finally getting something done about this skin condition..." By the end of the story, one actually felt sorry for the Joker!
He also suffers from this in Brian Azzarello's Joker. You can see it briefly when he trashes the bar after Harvey Dent doesn't take his phone call, but he finally reaches breaking point at the end when Batman turn his Breaking Speech back on him, causing him to fly into a blind rage and shoot his own loyal henchman.
Death of the Family: Joker spends the whole comic trying to prove to Batman his loved ones are only holding him back and after saving his Bat family has a brutal fight with him in the underground, Batman sets the Joker off by revealing his family makes him stronger
LIAR!!! YOU KNOW THEY DO ANYTHING BUT.
Dirk Anger of Nextwave spends the entire series going through a nervous breakdown. He thinks nobody noticed.
Long-time Justice Society of America foe Vandal Savage had a rather pitiful breakdown during One Year Later when faced with the possibility of imminent death for the first time in his millennia long lifetime.
Overlord from The Transformers: Last Stand of the Wreckers has the more subdued version. He's a nigh-unstoppable Decepticon deserter, whose main motive for desertion (or anything) was to goad Megatron into a one-on-one fight. He takes everything the Wreckers throw at him, even getting reduced to a burning endo-skeleton and keeps going... until Verity tells him that Megatron is dead, and the fight he spent his entire life preparing for will never happen. After that he just collapses and doesn't even put up a fight as they cart him off to prison. When we see him again in Transformers: More than Meets the Eye, he's gotten even worse; he no longer even moves or cares for himself, simply lying in his cell all day muttering "kill me" over and over.
Later in MTMTE, Overlord instantly recovers from the above-mentioned breakdown when he learns that Verity lied about Megatron's death. However he's than defeated through a different breakdown; Chromedome and Rodimus trigger his pathological fear of defeat. The second it seems like he's going to lose, he freaks out and starts giving a Rapid-Fire "No!" while cowering in fear, letting Fortress Maximus pound on him.
Also in MTMTE, Big Bad Tarn seems to be doing pretty good when he first appears in season 1. However when he reappears midway through season 2, we get a look inside his head and it's revealed that he's actually been having a worsening nervous breakdown, as his guilt and stress over his job and his addiction to transforming causes his mental state to worsen and his faith in his cause to falter. And than when he learns about Megatron's side-change and denouncement of the Decepticon movement, making everything he's done pointless, he snaps and attempts to commit suicide by drug overdose. Even when he recovers (somewhat) and refocuses on his goals, he becomes noticeably more unhinged and his trademark calm speeches turn into lengthy rants.
In Y: The Last Man, the opium smuggler Yorick befriends and falls for on the journey to Australia justifies her trade by reasoning that humanity is already doomed, and all she's doing is making people's lives easier by giving them an escape from this awful knowledge. Then, she realizes that Yorick's survival means that humanity has hope after all, and all she's done is make things worse by creating further misery and despair. She doesn'ttake it well.
Doctor Doom suffered a pretty huge one in one story. At one point he had Reed Richards imprisoned in a torture room full of mirrors placed in such a way that the warped reflections would drive anyone crazy. At the start, he's classic arrogant gloating Doom. By the end of the story a few issues later, he's beating the crap out of Reed while screaming and ranting about how much he hates Reed. The fight takes them to the torture room, and Reed removes Doom's mask. Seeing thousands of warped reflections of his own scarred face drives Doom insane.
In the Spider-Man storyline Ends of the Earth, it's revealed that the dying Doctor Octopus' grand scheme is to wipe out most of humanity, leaving about 0.08% of humanity to live and rebuild, remembering him as the greatest monster that ever lived. However, Spidey points out a glaring flaw in that plan: yes, 0.08% of humanity would live on - but his super weapon would flash fry their brains, leaving them brain dead. Faced with that glaring flaw, Octopus flips out, trying to see where he went wrong, giving Spidey the opportunity to take him out.
All of the Inner Circle by the end of X-Force: Necrosha, including the sympathetic members, have devolved into raving lunatics giving hammy speech after hammy speech about how they're going to kill everyone on Earth and remake it in their image.
At the end of Hellboy: Conqueror Worm, even though all his plans have failed and he is now nothing but a ghost, Rasputin still believes that he will be the one to release the Ogdru Jahad and bring about Ragnarok. However, he is confronted by the godess Hecate, who bluntly tells him that he is completely insignificant in the grand scheme of things, that Hellboy is the only one with the power that he seeks and that, even after summoning him to Earth, he has no control over him. Rasputin flies into such a rage that he appears to be on the verge of attacking Hecate before she obliterates him with a wave of her hand.
In the crossover Spider-Man / Batman, Carnage has a spectacular one. Near the end of the story, he has Batman at his mercy and Spidey unable to act. Then, The Joker reappears holding a Jack-In-The-Box and ready to pop it open and unleash a deadly virus, all because he won't let anyone else kill the Batman. Carnage, a mass murderer himself, flies into a magnificent panic and giving Batman the opening to free himself and take him down and allowing Spidey to stop the Joker.
Both Bane and Az-Bats suffer this during the Knightfall storyline. For Bane, the appearance of the Jean-Paul Valley Batman hadn't concerned him much, but after he was badly wounded, Bane decided to put this pretender to the throne out of his misery. Once JP is able to deliver a strike that severed his Venom feed, Bane panics and finds himself being kicked around and ultimately defeated. For Az-Bats, he was already suffering from Sanity Slippage thanks to the hallucinations of his father and Saint Dumas, but once he ends up letting Abbitoir die, he's finally lost it, ranting and raving how he's the one true Batman and that he hadn't failed in his "sacred mission".
Thanos tends to go nuts whenever anything endangers his relationship with Death. He stammers in disbelief when he realizes that the Power Infinite has made him too powerful to be with Deathnote he had to be equally powerful to Death, not more powerful, giving the heroes the opportunity to stop him. He throws a fit of jealousy and curses Deadpool with immortality when it seems like Death likes Wade better than him. Finally, when he learns that his Thanatos Gambit in The Thanos Imperative has rendered him immortal, meaning he can never be with Death, he loses all of his sanity and becomes so dedicated to destroying everything that he has to be sealed in another universe to stop him.
The Riddler has a grand one when he decides to deal with Impulse. After a bad encounter with The Flash and Robinnote Riddler had bailed from Gotham following the events of Batman: No Man's Land, Edward heads for Manchester to deal with Impulse, thinking he can easily outwit the protege of the Scarlet Speedster and one of the Boy Wonder's closest allies. Instead, poor Eddie is left a blabbering mess with Bart utterly ignores every sign that the Riddler wants him (too busy playing video games), Bart's inability to recognize who he was (he mistakes him for The Question, Mr. Freeze and Abra Kadabra), outwitting his traps without thinking (before he's done reading off his first clue, Bart comes back with the bombs by looking under every porch in town. And finds his other bombs while he was at it!) and ultimately saves his captives by retaping his last clue that he tore up. His comment after revealing the second set of bombs sells it, though:
The Riddler: "DO YOU THINK MERE SPEED CAN UNDO MY GLORIOUS INTELLECT? YOU'RE WRONG, I TELL YOU! WRONG, WRONG, WRONG!"
Monocle in Forever Evil out of paranoia. More notably, though, is Lex Luthor whose fears about super-humans come to life with the Crime Syndicate, and finally calls out for Superman's help.
In "Tried and Tse-tsed", after the tsetse fly Iznogoud plans to use to get the Caliph to go to sleep permanently is sedated by the Caliph's cup of herbal tea and adopted as a pet by the genial ruler, the vizier is reduced to a babbling wreck whom Wa'at Alahf is forced to have committed.
At the end of "The Lookalike", the Caliph and his doppelganger, Aristides Kingsizos, have met and bonded over a game of cards, and the formerly grouchy lookalike now talks and acts like the Caliph. On the palace steps, Iznogoud sobs to Wa'at Alahf that he tried to get rid of one Caliph and now he's stuck with two. Then Aristides' business partner comes looking for him... and he turns out to be a dead ringer for Iznogoud, who goes catatonic with shock.
Deadpool outcrazies Carnage by convincing him that he's just a character in a story written by someone else with no real control over his life. Carnage falls into a Villainous B.S.O.D. so severe that he lets himself be incarcerated and refuses to leave until he can be sure he has free will again. One police officer notes that the door to his cell isn't even locked.
When Agent Venom foils the schemes of the previously suave and relaxed Crime Master and Crime Master's sister makes clear that she wants nothing to do with him, he loses his cool and attacks Flash while screaming about how he ruined everything. When it seems like he might be winning the ensuing fight, he devolves into arrogant ranting about how his plan will work so much better the second time.
In Locke & Key, Dodge is genuinely panic-stricken for the first time when Tyler reveals his newly-created Alpha Key, that can unlock demons from souls.
Kingdok in Bone starts the comic as a well put together and clever fellow. But as the comic goes he suffers an increasingly long series of humiliations, beatings, and failures; he loses his arm in a fight, gets mauled by Rock Jaw, is repeatedly humiliated in front of his men by the Hooded One, gets trapped alone underground for nearly a month, and more. Alongside this, his mental state degrades more and more, reducing him from a well-spoken tactician to a half-crippled mess. By the time the heroes face him for the last time, he's crossed the Despair Event Horizon and only attacks them to make Rose kill him.
One of the creepiest things about this breakdown is how the art symbolizes it. At the comic's start Kingdok is drawn to look rather slim and friendly. As his breakdown worsens, he's drawn progressively more ugly and monstrous, as if his very body is being warped by the abuses he's suffering.
In issue 75 of The Transformers, when Optimus opens the life-creating Matrix inside of Unicron, triggering the latter's destruction, the supposedly unstoppable Eldritch Abomination proceeds to completely lose his shit. These are his last lines of dialogue before he explodes:
"NOOOO!! NOOOOOOOOOO!!! IT BURNS!!! WHITEWHITEWHITE! I AM FILLED WITH LIFE- TERRIBLE, WONDERFULLIFE! THOUGHTSFEARSDOUBTSPAINLOVEDEATHTOOMUCHTOO-"
Black Moon Chronicles: At the final confrontation with Wismerhill in the imperial castle, Haazheel finally goes apeshit when his soldiers start to lose, going One-Winged Angel and destroying anything he sees.
The tenth and final issue of the Madballs comic book published by defunct Marvel Comics subsidiary Star Comics had a rare example of the villain having his breakdown at the very start of the story. When the Madballs Bash Brain, Touchdown Terror, and Fist Face walk in on Dr. Frankenbeans before he has a chance to act out his latest scheme in defeating them, Frankenbeans responds by throwing a tantrum over how it isn't fair that the Madballs always win. The doctor's outburst causes him to fall ill, afterwards Snivelitch begs the Madballs to save Frankenbeans' life.
Dark Annisia begins Red Sonja: Queen of Plagues as a Well-Intentioned Extremist combating a plague by slaughtering the infected. She escalates to besieging a healthy city after it finds a cure and executing those who violate her open-ended quarantine. After the plague's true cause and her part in it are revealed she snaps into full-on bloodthirsty madness.