A challenge is overcome due to a character's specific quirk of insanity. Their inability to handle normal reality has been weaponized into an effective means of solving one or more problems. Keep in mind, this character's madness is essential to the task. A saner version would have failed.
This type of useful insanity is usually Played for Laughs. In Real Life we would expect these characters to get fired, arrested, and eventually hospitalized or killed. Not so in the world of fiction; these characters have been able to achieve things their saner counterparts are unable to, similar to Achievements in Ignorance. They're often as entertaining as a Bunny-Ears Lawyer, who is a capable character despite or alongside their quirks.
If their insanity prevents them from being killed or arrested when anyone else would be, that's a Lunatic Loophole. If a character's quirky but not actually insane, they're a Bunny-Ears Lawyer. If the bad thing that happened was so bizarre that they're the only person prepared for it, they're Crazy-Prepared. When all of humanity is composed of Heroic Madmen, that's Humanity Is Insane. If the crazy person was right about something, that's The Cuckoolander Was Right. If they gained any powers from their insanity, that's Power Born of Madness. When a crazy person is in a position of power, that's The Wonka.
Contrast Sanity Has Advantages.
- Continuity Comics: Crazyman, whose power is being crazy. "Crazyman" is recruited by a secret service as the "Plan B" to dangerous "unwinnable" situations. Danny is to the secret service as Monk is to the San Francisco Police Department, and comes up with solutions no sane man would come up with. If James Bond were insane, he'd be Crazyman.
- The Joker: A villainous example. A great deal of what the Joker does should be impossible. He has a tiny fraction of Batman's resources, doesn't have his own Charles Atlas Superpower to match, has a reputation that should make it impossible for him to secure allies and minions, and his scientific knowledge, while great, is limited to "realistic" inventions (unlike, say, Lex Luthor). And he's still one of the most successful (and terrifying) villains in the DC Universe, because insanity is his super power.
- The Sandman: One story has Delirium in a foul mood, having hidden herself away in her realm and cut off all access. In order to get to her, Dream recruits several mentally ill people, as only their flexible interpretations of reality would allow them to navigate Delirium's home unscathed.
- Common joke among Mathematics or Computer Science students and professors involves asking how many people became insane while studying in their departments. The correct answer is zero: insanity is a prerequisite.
- The main character's severe autism means he's the only one able to objectively synthesize all of the information and determine just what the deal is with the Starfish Aliens they discover. Of course he's also unable to bond with other people or empathize with them, so...downer.
- The predatory instincts and complete sociopath nature of the ship's captain (who is an actual vampire) also turns out to be vital in second-guessing the otherwise indecipherable behavior of the alien vessel and its inhabitants.
- Jonathan Strange & Mr Norrell: The eponymous Strange must drink a bottle of distilled madness (causing him to lose his mind) in order to be able to see and interact with The Fair Folk on their own terms.
- Madness Has Its Place by Larry Niven: Jack Strather's megalomania and paranoid schizophrenia make him one of the few men left on Earth with the cojones to actually resist the invading Kzinti.
- "The Men Return" by Jack Vance: The short story featured a world where causality had basically gone out the window. One character was barely surviving, trying to find patterns where there were none. The ones who were crazy before The Event on the other hand were basically gods.
- Never Let Me Sleep: Whether it's the way her brain naturally works, or the medication she takes for her disorders, Melissa is the only person not effected by the death sleep within the "South Dakota Quarantine Zone".
- Redwall: In High Rhulain, the hare Major Cuthbert went insane after his daughter was killed by vermin. He ended up killing a sea monster single handedly.
- This Alien Shore by C.S. Friedman: The Guerans (a mutant race descended from humanity) are all insane, which makes them the only ones who can pilot ships through hyperspace. In addition, the heroine's multiple personality disorder grants her a secret power that could alter the balance of power throughout known space.
- Deconstructed in Law & Order: Criminal Intent. Detective Robert Goren was encouraged by mentor Declan Gage to indulge his darker impulses to help him understand the criminal mind, and for a long time this approach served him well. However, after a particularly grueling season, he learned that Gage was manipulating events in order to kill Goren's brother and his nemesis, convinced that Goren would be a better detective with fewer people in his life to distract him. Instead, it drove Goren into a psychotic break.
- The premise of Monk is that Adrian Monk's obsessive-compulsive disorder allows him to notice details that normal people would miss, allowing him to solve crimes that stump the police.
- Seven Days: The only person able to pilot the Chronosphere is Frank Parker, inmate at a military insane asylum.
- Call of Cthulhu: There's a rule concerning "Insane Insight" that allows a PC going mad to obtain some hint from the GM as to what they're dealing with or the true natures of the cosmos.
- Dead Space: Isaac Clarke has the blueprints of the Marker in his head. This makes him the perfect guy to go about killing the source(s) of the Necromorphs, and allows him to read and decipher Marker texts. It also makes him paranoid, schizophrenic, and he often hallucinates dead people talking to him. Which is pretty par for the course for anyone who's survived close contact with a Marker, to be fair.
- Hatoful Boyfriend: Anghel Higure is trapped in a delusion that his life is some high-fantasy epic story and those around him are characters in the same. His fantasy stories are, in fact, a perfect metaphor for some of the other characters' personal storylines, including some very dark secrets about them that not even they know, the "spores" he rambles about are probably the biological superweapon samples the doctor has in the clinic, and his senses are highly sharpened by the paranoia of believing himself a fantastical antihero, enabling him to detect threats sooner even if he can't always communicate them.
- Portal: Schizophrenic Doug Rattman was completely right in suspecting the operating system was out to kill everyone and so was the only survivor of the lab incident.
- The Secret World: Daimon is a firm believer in this, hence his astonishingly eccentric behaviour. As he explains in both dialogue options and cutscenes, he believes that only individuals who are utterly without structure, dignity and sanity can truly succeed in the dark days, and to this end has made himself as loose, adaptable and eccentric as possible. He even compares this to incidents where drunk-drivers somehow manage to survive accidents that would have killed sober motorists, reasoning that their survival is due to having lost all the self-respect that might have made them brittle, instead being malleable enough to walk away unharmed.