In The Affix Matt is driven off the rails a bit by the sheer inanity of his circumstances: saddled with a gem that blows up probability and won't let him get rid of it, accosted constantly by dangerous believers in the supernatural that he thinks are crazy, and perpetually short on sleep. After a day or so of this he gives up on trying to make much sense of it and gets openly hostile towards his antagonists, and as a result he becomes fairly dangerous in his own right.
In And Then There Were None, Vera Claythorne becomes increasingly consumed by paranoia and guilt and is so psychologically broken by the end of the book that she willingly hangs herself with the noose the killer sets up for her.
Black Tide Rising: In Under a Graveyard Sky, Faith goes a little into this after they board a yacht that was taken over by the mercenaries hired to protect it and sees the carnage that followed, killing and rape everyone there. It becomes more serious when they're clearing a cruise ship later. Oddly it's not fighting zombies that does it but what she finds after the zombies are cleared out, the horror shows in the cabins, even the ones where they find survivors. She turns Trixie, a teddy bear they found on one ship into a Companion Cube as a coping mechanism.
Jaimy in the Bloody Jack series. Early in My Bonny Light Horseman, he receives a head wound in battle that doesn't get treated for weeks because he's in a French prison. As the series progresses, you can see him slowly spiraling down to his Heroic BSoD in The Mark of the Golden Dragon.
Duane Hoover in Kurt Vonnegut's Breakfast of Champions gradually loses his sanity throughout the novel and is pushed over the edge when he takes a Kilgore Trout short story as the truth and believes he is the only real person on Earth.
Bulldog Drummond series: Irma, the Big Bad Peterson's Dark Mistress, goes off the edge completely after Peterson dies. She talks to a bust of Peterson, and even some of her henchmen doubt whether it was a good idea to continue with her.
The Bursar of Unseen University from Discworld used to be quite sane, up until the appointment of Mustrum Ridcully to Archchancellor wore away at his nerves. His sanity really took a dive in Reaper Man, when ancient wizard Windle Poons rose from the grave. In fact, it's so bad that the medication he's given is specially designed to make him hallucinate sanity.
In the original Dracula, Jonathan Harker and Renfield experienced this thanks to the Count. Harker recovered; Renfield, not so much. Renfield started out as a mental patient with a fixation on eating life. Dracula makes him considerably worse, but Renfield does recover enough to try and save Mina from Dracula though he's killed for his trouble.
In Dragon Bones, Ward's mother is already a Cloudcuckoolander at the start of the novel, but gets worse over the course of it. In the end Ward can't find her anymore with his magical ability to find people, even though her body is there. She's gentle and nice the whole time, but lives in a world of her own making, and refuses to acknowledge the reality (which is not really worth living in, at least before the death of her abusive husband).
In the Dreamblood Duology, part of a Gatherer's disintegration towards becoming a Reaper is losing their mind. Ehiru has violent thoughts and dreams while suffering from dreamblood withdrawal.
The titular character in Eden Green considers herself a rationalist, but as she investigates the alien needle symbiote infesting the body of her best friend, her grasp on reality gradually begins to slip.
Poor Sirius was showing signs of this even before he got put into Azkaban, with his Laughing Mad display after Peter framed him and escaped. Prisoner of Azkaban proves his time in the wizarding prison did him no favors, and while he started to recover during Goblet of Fire after being put under house arrest for his own protection in Order of the Phoenix he starts slowly slipping again.
In Harry Potter and the Philosopher's Stone, Vernon Dursley slowly starts to lose his grip on things as more and more Hogwarts acceptance letters arrive for Harry Potter, nailing up the mail lot, tossing letters in the fireplace and eventually taking the whole family to a deserted island in the middle of a terrible storm in the hopes of getting away. In the film, you can even see that his normally carefully-maintained hair now looks wild.
Dudley: Daddy's gone mad, hasn't he?!
The Big Bad of the Heralds of Valdemar series suffers steadily worsening sanity as he Body Surfs through the centuries, as a result of spending his time between bodies in a Soul Jar in the Void Between the Worlds. As Ma'ar and Leareth he's a fairly Magnificent Bastard, but by the time we see him as Mornelith Falconsbane in the Winds trilogy he's grabbed the Villain Ball tight and won't let go. The slippage accelerates when he's flung into the Void bodily between Winds of Change and Winds of Fury, leading to his final downfall.
A consequence of syphilis in The Kingdom of Little Wounds. The queen has probably been losing her mind for years, and she only appears to get worse over the story.
Gollum and Denethor in The Lord of the Rings. Also, Isildur after he gets the Ring. Boromir, particularly after Lórien.
What, you forgot Frodo?
Thorin deserves a mention, his desire for gold applied this trope to him. Thankfully he regains it in the end.
Very common in H. P. Lovecraft's work, most notably in "The Rats in the Walls" and "The Shadow Over Innsmouth". Of course, considering the type of stories he wrote, it's understandable. (Although both of those are actually feature a less cosmic form of horror, with the respective protagonists each finding something unpleasant wiggling in the roots of his family tree.)
The Luminous Dead: Gyre becomes an Unreliable Narrator over weeks of solitude, claustrophobia, and dangerously limited supplies as she explores a cave system that's killed dozens of earlier cavers. Worse, she knows her mind's going, but can't always tell what is and isn't real.
In Max Barry's Machine Man, the main character, Dr. Charles Neumann, suffers from this. While not quite "normal" to begin with, after he's replaced both legs and one hand with Better Parts, he starts talking to them and referring to himself as "we".
In The Magicians, this is a common response of students to the fourth year at Brakebills, for a variety of reasons: first of all, they're studying in Antarctica this year, and the monotony of the landscape can be mind-numbing; secondly, they've been magically prevented from speaking or communicating, driving some to almost Go Mad from the Isolation; thirdly, the learning process itself is a sanity-shredding series of Wax On, Wax Off exercises designed to internalize the Magic Prerequisites, and presided over by a Sadist Teacher. As such, several students just snap and start randomly fucking each other in public, so desperate for any kind of human contact that they no longer care who sees them. Meanwhile, Quentin loses his grip on the passage of time and starts hallucinating at length, even resorting to talking to absent friends during the marathon to the South Pole. Fortunately, most recover quite ready upon returning to the main campus.
In the Newsflesh series, Shaun has a bad case of slippage after being forced to shoot his sister when she's going into amplification, i.e. becoming a zombie at the end of the first book, Feed. Over the course of the next two, Deadline and Blackout, he goes from having conversations with Georgia to outright visual and tactile hallucinations. He's well aware he's clinically insane, and prefers it to sanity, since dealing with the reality of his situation would push him to suicide.
Happens to a few characters in The Pale King, most notably David Cusk and Lane Dean.
Most Redwall books have at least one villainous character go through this.
Alex: becoming a Psycho for Hire for whoever holds the power - though truth be told, he just needed a little push
Isobel: completely breaking down from Joy's Mind Rape - which we get to read in painful detail... except the "therapy reports" are written completely in newspeak.
Louis: getting more and more lost in his vision of the Revolution, overlooking obvious flaws until everything collapses around him
Joy: a meek girl with self-image problems, using her intelligence to get to power and ending a Knight Templar. Then she realises that she could actually have a boyfriend and it drives her completely Yandere over a couple of chapters.
Michael, the most notable, being the narrator: over a couple of chapters he suffers severe head trauma, discovers alcohol, discovers that the girl of his dreams is a slut and what's worse, she only started an affair with him to get back at his brother... he starts hearing voices, having memory gaps... By the end of the story he is so broken, that when he discovers what he is now a boyfriend to a Yandere and they just murdered his ex in cold blood , he decides to just roll with it.
Louis Creed in Pet Sematary. Quite understandable since he's lost his son, brought him back to life, was forced to kill him again, and repeats the process with his dead wife.
Stephen King loves this trope. Bag of Bones and the short story "The Ballad of the Flexible Bullet" are about men who clawed their way back from the brink of insanity. The short story "The Jaunt" is about a teleportation machine that causes insanity if it is used incorrectly.
Theon's Point of View chapters in A Clash of Kings show him becoming increasingly more terrified and paranoid, making ever more desperate decisions as he realizes that the reinforcements he needs aren't forthcoming.
While Cersei had never been completely grounded, she wasn't completely off her rocker either. Over the course of the fourth book, though, in response to the death of her firstbornson and shortly afterward her father as well, she starts losing it, seeing enemies in every corner and ordering people tortured willy-nilly.
Arya Stark becomes more and more unhinged after her situation just keeps getting worse with no end in sight.
Catelyn Stark has a weird variation of this. Early in the first book, she goes into a borderline-psychotic state after major trauma, deeply disturbing everyone around her. She quickly snaps out of it, and from that point on seems okay, but her POV chapters show her becoming increasingly depressed and revenge-driven. She finally snaps when she watches her firstborn son murdered in front of her eyes, which drives her completely insane, shortly before she's murdered herself. When she's brought Back from the Dead, it's... not pretty.
In the X-Wing Series Lara Notsil, AKA the former Imperial agent Gara Petothel, slowly goes through one as she becomes the mask after infiltrating Wraith Squadron. It turns out that Imperial Intelligence was... lax in concerning themselves with what would happen to an agent after having so many different identities swirling around in their head. She manages to never show it, but some of her inner dialogue is downright depressing as she fights between her two /three different identities in order to stay with her Squadron.
Palpatine from Dark Empire. Pre-Endor Palpatine had been scarily sane, but the ordeals of death, Body Surfing, and the natural mental instability of clones leads him further down the slope throughout the course of the story.
In Timothy Zahn's Thrawn Trilogy, Joruus C'Baoth was always insane, but generally did a good job keeping that fact concealed. His control slips drastically by The Last Command.
Szeth-son-son-Vallano is a pacifist who is also a Truthless—a sort of warrior-slave of his people, bound to obey anyone who holds his Oathstone. He is also quite possibly literally the most dangerous man on the planet, partly because he's the first Surgebinder to be seen in four thousand years. He, understandably, is typically used as a weapon and assassin, which is made worse by the fact that there is nothing magical about his oath; he could stop the murders at any moment if he would just choose what is right over the law. By the second book, his brain is barely hanging on by a thread. It gets worse when he finds out that the "lies" he told that got him made Truthless were actually true all along, meaning absolutely none of it was necessary.
The Heralds, who have been wandering the world for four thousand years after giving up on their oaths, are getting crazier. Shalash (Herald of Beauty) has taken to destroying any artwork depicting her, Nale (Herald of Justice) is obsessed with law to the point of being willing to kill a girl over petty theft—but stopping the instant she is pardoned, and Kalak has become a paranoid wreck jumping at shadows.
Kalak: I'm worried about Ash. Nale: You're worried about everything. Kalak: She's getting worse. We weren't supposed to get worse. Am I getting worse? I think I feel worse.
Elaborating on Nale, he's seen the same signs of the upcoming Desolation Szeth did, but refuses to believe them, and his sanity is suffering as a result of him trying to believe his own lies.
Stravaganza: Over the course of books five and six, City of Ships and City of Swords, Grand Duke Fabrizio di Chimici, the main antagonist, starts to suffer this. Of course, his beloved younger sister running away and eventually marrying a member of the family the di Chimicis are archenemies with, and things just generally going wrong on a regular basis, doesn't help.
In Thérèse Raquin, the more time passes, the more Thérèse and Laurent are haunted by memories of Camille, and the crazier they become.
Sylvester in Twig is a Tyke Bomb who was given massive doses of Wyvern, a drug designed to allow rapid learning by increasing brain plasticity. The amount Sylvester received allows him to pick up new skills very fast, analyze people quickly and make up excellent plans on the fly. However, his brain will eventually degrade as the Wyvern breaks down parts of the brain which really need to be in one piece. Around the middle of the book, Sylvester begins seeing hallucinations of his absent friends. Then he starts hallucinating his dead enemies. Then the hallucinations start attacking.
In Fall of Damnos, Sahteh the Enfleshed, a lord of Necron Flayed Ones, finds himself less and less self-aware as his craving for a new skin grows stronger. By the end, he can't tell whether he's still alive or already a killer robot, doesn't know what planet he's on and thinks of nothing but getting a new skin.
In the Horus Heresy novel Vulkan Lives, Vulkan is captured by Konrad Curze, who repeatedly tortures and kills him in an effort to break his spirit. These constant torments gradually erode Vulkans sanity, causing him to hallucinate that his dead brother Ferrus Manus is mocking him. By the next book in the series, hes been reduced to a near-feral state where he cant tell friend from foe and lashes out at everyone around him. His sanity is ultimately restored in Deathfire.
After her deputy Tigerclaw betrays her, this occurs to Bluestar in the first arc. She started out as The Woman Wearing the Queenly Mask however began becoming increasingly unstable after the incident. She spent most of her time in her nest, frequently had an unfocused, glazed look in her eye, and became snappy. Bluestar began to become paranoid that essentially every cat was out to get her and even thought StarClan was plotting against her. She became more like herself right before losing herlast life.
Rand Al'Thor of The Wheel of Time certainly seems to inhabit this trope over the course of at least seven Doorstoppers. More pressures, more sacrifices and mistakes, more obvious signs of mental instability. After he is almost captured by legendary psychopathic torturer Semirhage and forced to almost kill Min he snaps completely. He adopts Dissonant Serenity and engages in more and more questionable deeds. After almost killing his own father, willingly, out of misplaced rage and paranoia, followed by a bit of fatalist Straw Nihilist monologuing on the site of his death in a previous incarnation 3,000 years earlier he seems to be showing signs of addressing the slippage though.
The Witchlands: In book two, Windwitch, Merik's sanity takes a beating when he's maddened with grief and in constant pain from the wounds he received at the hands of a would-be assassin. Most notably, he goes from trying to find the evidence needed to apprehend his sister to trying to find an excuse to kill her. Thankfully, he manages to regain his sanity.
The narrator of "The Yellow Wallpaper". Understandable, when you're locked in the attic for months, almost totally deprived of outside interaction.
Of course, a popular theory is that the "attic" in question is actually a room in a mental hospital, and that the narrator is already insane when the story begins.