The Killing Joke is one take on the Sanity Slippage that eventually led to the origin of The Joker. But the Joker admits he's an Unreliable Narrator and could be remembering wrong or making the whole thing up. He attempts something similar to crack Commissioner Gordon. He doesn't succeed.
Jackson Georges from Ex Machina, Mayor Hundred's former NSA handler fits this trope. In flashbacks the reader is shown how the cryptic shard that Mitchell found when he got his powers slowly drives Jackson to levels of extreme paranoia. He develops an unfounded contempt for Mitchell, claiming that without Mitchell's appearance and the mystery of the shard, he could have foreseen and prevented 9/11. He becomes obsessed with protecting his family from dirty bombs and the like, buying a Hazmat Suit and making tally marks on the wall to represent god knows what. It's clear he's a step away from the deep end. Darkly subverted when in desperation to save their failing marriage, his wife breaks into his work shed and steals the shard. A few seconds near a TV are enough to drive her completely and utterly insane, leading her to kill her daughter, husband, and dog. She even chops off her own arm with the shard itself. It was an incredibly jarring and brutal twist on the slow burn of paranoia the reader had been witnessing for months.
J. Jonah Jameson from Spider Man suffered a nervous breakdown late in Marv Wolfman's run, to the point where he believed Spider-Man was stalking him. However, Wolfman left the book before long, and Roger Stern retconned the whole thing away as mind-control.
Jean-Paul Valley's stint as Batman during the "Knightquest" portion of the Knightfall storyline was this. After being doused with the Scarecrow's Fear Gas, the hypnotic trance known as The System kicked in, haunting Jean-Paul with images of his father and of Saint Dumas, the "creator" of the order he once was part of. As he's haunted by these apparitions, The System drives him to be more brutal and continuously modify the Bat-Costume, the pinnacle being when he allowed Abbatoir to die, condemning his captive to death, modifying the Bat-Costume to the point where it was less Batman and more Azrael and outright alienating Robin, Commissioner Gordon, and Bruce Wayne and deciding that all criminals need to be put out of their misery. It's at that point that Bruce decides enough is enough and sets out to take back the Mantle of the Bat.
Fan Works
Jack O'Lantern, the Arch-Enemy of Spider-Woman, commits increasingly violent and destructive crimes as the series progresses. He goes from robbing banks to taking people hostage to going on killing sprees to orchestrating a bloody city-wide Mob War. Even in jail, we see him fantasizing about carving up human heads the way people do Halloween pumpkins. What's unusual is that Jack always had these sadistic urges-the Sanity Slippage comes from the escalating nature of his crimes.
Austria/Roderich Edelstein in the 1983:Doomsday Stories is portrayed for the most part as undergoing through this. His obsession in finding out whether Hungary survivedDoomsday grows increasingly desperate (and irrepressible) over time to the point that others eventually start wondering if he's gone delusional from grief. He doesn't. It's also mentioned to have happened as well with Romano (hijacked by The Mafia as his brother's successor) and Poland (having his personality shattered).
In the vein of the Cutie Mark Failure Insanity Syndrome described below, The Audience by Reality Check states that Trixie herself is diving into one as her special talent isn't magic like most unicorns, but rather stage magic, illusions and theatrical personalities. The constant heckling, jeers and challenges towards her achievements that she was receiving were making her the Jerk Ass that she was portrayed as in canon.
Total Drama Stranded: Briony gets a major one very quickly when Calvin begins relentlessly bullying her.
Songs about going insane are quite common, actually. Many examples at Sanity Slippage Song.
"Stan" by Eminem shows the story of a fanboy with a seriously screwed-up life and a downward spiraling sanity. The video starts with Stan bleaching his hair just like Eminem's, then Stan starts writing letters to him every so often in his room all plastered with posters of Eminem, then he sends Eminem a really pissed off letter complaining about how he missed Stan and his brother at a gig. When his pregnant girlfriend scolds him for wasting his day on watching Eminem, that's the final straw on the back, and he ends up tearing all his posters, tying his girlfriend in his car's trunk, and driving off a bridge.
Then Eminem sends back a letter, and starts by apologizing for how long it's taken him to finally respond. Trippin'. Best part: In his response letter, Eminem decides to cite a story he heard on the news about a guy who drove his car off a bridge with his pregnant girlfriend in the trunk, in the hopes that it'll get Stan to calm down a bit. Then Eminem realizes the news story was about Stan. "Damn," indeed.
The Violent Femmes' "Country Death Song" is pure American Gothic: rural guy goes mad from isolation and boredom, throws his little daughter down a well, then broods over his guilt till...you can probably imagine.
Pink Floyd's The Wall chronicles a man slowly alienating himself from the world, causing his mind to collapse on itself until finally what's left of his sanity stages an intervention and forces him to actually deal with his problems.
The band's previous albums, The Dark Side Of The Moon and (especially) Wish You Were Here, were inspired by the real-life sanity slippage of former bandleader Syd Barrett, who had become impossible to work with. "Now there's a look in your eyes / like black holes in the sky". His former bandmates reluctantly dropped him and felt guilty about it ever after. The two albums were enormously successful, but the subsequent non-stop grind of touring to unappreciative audiences caused Roger Waters to suffer a sanity slippage of his own, which directly inspired The Wall. Which was an even more enormous success!
By Coheed And Cambria's third album, the author in the frame story of their sci-fi epic has started talking to a bicycle and making both death threats and declarations of love to the ex-lover for whom he wrote the story. In the previous albums the author was not a significant character, and the only real sign of his instability was the fact he was writing the kind of material you can make a Prog Rock Concept Album out of.
Gorillaz: Both Murdoc and 2D show signs of this as of phase 3, rambling and gibbering like never before. 2D seems a bit sharper than earlier chapters, though, while Murdoc's just gotten bolder and more malevolent.
Professional Wrestling
R-Truth turned heel after losing out on a WWE Championship opportunity. And after that, his mind.
Daniel Bryan. Yes! Yes! Yes! Yes! Yes! And after AJ Lee left him at the altar, it turned into: No! No! No! No! No!
A daily occurrence in Warhammer and Warhammer 40000; living in an endlessly terrible Crapsack World will do that. Witches/psykers are especially vulnerable to Slippage, thanks to the source of their powers being the home of The Legions of Hell.
Also appears in Warhammer Fantasy Roleplay, it has a mechanic for going insane and lists quite a nice amount of mental illnesses for which your character can suffer
As befits its source material, Gaiden GameDark Heresy has mechanics by which players can go insane.
Call Of Cthulhu is famous for introducing the SAN attribute, which drops a little each time the players encounter a monster or cast a spell, or something.
Everyone in New World of Darkness, from normal humans to blood-hungry vampires to reality-bending mages, has a Karma Meter. As you slide down the slippery slope, you tend to become a little more unstable with each step, until finally, humans are reduced to raving lunatics, vampires and werewolves go nuts and become meat-hungry animals, mages and changelings fly off the deep end and lose the ability to separate reality from fantasy, and prometheans lose hope of ever becoming humans.
The fan-made World of Darkness game Genius The Transgression is unique in that players start out insane by nature of their profession, and as they lose Obligation start unconsciously altering reality to fit their delusions.
The Solars gradually experience this as they become more and more godlike, from both the Great Curse and general detachment from humanity and less powerful divine beings.
Being close to a Primordial War survivor in the First Age can be dangerous, humiliating, and bad for your physical, mental, and social health.
Also happens to Infernals. They have access to Yozi Charms. Everything the Yozis are, is made of Charms. Most of the Yozis are insane, and their Charmsets tend to be arranged so that the good stuff with no drawbacks is padlocked by something with benefits that makes you a little crazier. The best example of this is Kimbery, who has an entire Charm tree (built on The Power of Hate) locked behind something that permanently skews the sanity of its user to be either more naive or more vindictive, depending on the chosen variant.
In Fading Suns, Psychics and Theurgists are prone to "Urge" and "Hubris" respectively.
Characters in Eclipse Phase are very hard to kill permanently due to cortical stacks and backups, fortunately for GMs there's a mechanic called "stress points" that can cause psychological disorders or permanent catatonia if the PC lets them accumulate.
The title character of The Phantom of the Opera, though your mileage may vary on how sane he was to begin with. But he's definitely completely off the beam by the end, determined to have Christine at all costs, even if he has to blackmail her into marriage by threatening to kill her lover.
Web Comics
Jack from Gunnerkrigg Court. He started off as a pretty normal guy, then he briefly got pulled into a Dark World and saw some very unpleasant things. Since then he became increasingly antisocial, paranoid (at one point he starves himself because he's convinced the Court has laced his food with nanobots to track him) and amoral (compare his treatment of the Laser Cows to his treatment of the Guard Robot). Heck, even his appearance became worse over time.◊ Fortunately, now that the whitelegs is out of his head, he's gotten almost back to normal. Oh, and he was rightabout the food.
Vaarsuvius spent most of "Don't Split The Party" undergoing this in The Order of the Stick. They ultimately recovered.
Jin of Wapsi Square suffers from a bad case of this after destroying the calendar machine. It was actually built at least partially for the purpose of keeping her sane.
Karkat starts getting shades of this after a particularly brutal Trauma Conga Line. Two of his friends were murdered in from of his eyes, two others are on killing sprees, he's dragging his newly-blinded friend's body (and accidentally drops him down some stairs, and he gets a message from his girlfriend, pronouncing the details of another murder - and when he tries to contact her, one of the Ax Crazy trolls responds, hinting that she's been killed.
There. Good as new, best friend! It's like it never happened. No one can ever blame you for dropping him down the stairs now. Stairs? What stairs! Ha ha ha!
And now Rose is showing signs of it too, now that her mother's died.