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 machine that causes insanity if it is used incorrectly.
Roland goes through this in the first third or so of The Waste Lands due to the paradox he created by preventing Jake's (first) death in The Drawing of the Three. He gets better after being reunited with Jake.
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.
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.
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.
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.
Warrior Cats: Hollyleaf, and to a lesser extent, her brothers. Bluestar in the original series also goes though this after Tigerclaw's betrayal.
Most Redwall books have at least one villainous character go through this.
Happens to a few characters in The Pale King, most notably David Cusk and Lane Dean.
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".
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.
In Thérèse Raquin, the more time passes, the more Thérèse and Laurent are haunted by memories of Camille, and the crazier they become.
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.
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.
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.
Star Wars Expanded Universe: Lara Notsil, 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.
Another Star Wars EU example is 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.
Happens to Ron in the last Harry Potter book, whenever he wears the locket.
Katniss Everdeen progressively starts to lose it over the course of The Hunger Games trilogy.
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.
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.
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.