The Wonka is a genius nut who should, by all logic, be fired. That's never going to happen — The Wonkaruns the show.
In every society, things are done in certain ways. There are social conventions that have to be followed, logic patterns that always get applied, and priorities that are shared. Just don't expect a Wonka to take any notice. By extension, don't expect their employees to notice either because they're too used to their boss' eccentricity. They may or may not be normal in themselves but their boss will appear to be out of their mind.
Appear to be out of their mind. "There's a fine line between genius and insanity" and the Wonka clog dances on it. He makes perfect sense to himself (and it is usually male, although female examples do exist), but utterly confuses those around him to the point of them wondering whether or not he really is all there. The Naïve Newcomer will think he's genuinely nuts until he does something amazing that proves he's merely using a different brand of logic. Long term employees will either groan at the craziness, become like him, or be so desentitize they'll regard it as mundane and pay no attention.
These sort of characters are usually Freakish Loners, but if they do have friends, they will be close ones. Genius qualities do not a Wonka make, but they must show some sort of prowess in at least one area in order to confirm that they are in fact not mad, but merely "differently sane". Other common traits include irreverence, lack of social skill or any sense of danger and doing bizarre things that, nevertheless, make perfect sense if you take a step back and think outside the box, because that's where Wonkas live. From a psychological standpoint, The Wonka perfectly characterizes the schizotypal personality.
Different from a Cloudcuckoolander in that Wonkas have their heads in Loonyland and their feet on earth, whereas Cloudcuckoolanders are completely in orbit. Also, Wonkas tend to be more extroverted and energetic than drifty, dreamy Cloudcuckoolanders, and they tend to be more grounded in logic, even if it's of the "lateral thinking" sort. For example, a Cloudcuckoolander may carry a gas mask around once to scare away evil spirits, but a Wonka will carry a gas mask around everywhere "in case there's a gas leak. Duh," and then act as though you're the odd one because you don't.
Also different from Bunny-Ears Lawyer in that the lawyer is a brilliant employee who isn't fired because they are so good at their job. Tolerating their weird mannerisms and unusual quirks is worth it for the work they do. They win a cost/benefit analysis. The Wonka is a brilliant employer and can't be fired because they own the company. Also the Wonka's unusual brand of sanity is likely the reason for their success while success and quirks are unrelated in the Bunny-Ears Lawyer.
If you have a case where The Wonka indeed runs the ''entire'' show, you have The King of All Cosmos.
If the roles are reversed such that The Wonka is the one who's the normal one and it's everyone else who's crazy, you've got the Only Sane Man.
Compare with Inexplicably Awesome and Eccentric Mentor. Contrast with Genius Ditz and Obfuscating Insanity. (Wonkas don't have an act to drop.) Also contrast The Caligula, where being mad and powerful makes the person a danger to himself and others.
Please note that this trope doesn't necessarily apply to parodies of Willy Wonka himself. For that kind of trope, please see Charlie and the Chocolate Parody.
Examples:
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Anime and Manga
The eponymous Irresponsible Captain Tylor is this through and through. His idiosyncrasies annoy his commanders so much that when they gave him a medal, they put a bomb in it.
Bleach: Kisuke Urahara, the owner of a candy shop is this in spades. He seems childish and a little crazy but he's a brilliant scientist and a captain level shinigami. The fact that he owns a candy shop could be a subtle reference to the trope namer.
The anime sometimes uses filler comedy to turn Badass Grandpa Yamamoto into one.
Pegasus, the brilliant but loopy creator of Yu-Gi-Oh!'s Duel Monsters. His employees take his eccentrics in stride. (Note that he was indeed a villain originally, and did use some rather immoral methods; he got better.)
Niizuma Eiji from Bakuman。 knows as much about creating brilliant manga as he doesn't about normal behaviour.
Shinra's father in Durarara!!. Apparently a relatively well-respected doctor, he goes around everywhere with his lab coat on and a gas mask. After all, everyone knows lab coats protect your body from contamination (that's why you wear them in the lab) and modern-day city air is so filthy it's bad for your lungs.
Monkey D. Luffy may not be a loner, but he's The Captain and definitely operates on an entirely different wavelength compared to normal people.
Minaka Hiroto from Sekirei is a brilliant scientist and the CEO of a powerful Mega Corp. He also runs around in a cape because he can, and organized the entire Sekirei Plan because It Amused Me. His second-in-command and secretly his former(?) lover, Takami, spends a lot of time hitting him with things.
Comics
Reed Richards of the Fantastic Four drifts near to this trope sometimes. His wife usually has to reel him back in.
John Porter of Damage Control. Given the nature of the cases they have to deal with, it's understandable.
Rotor Walrus from Archie Comics' Sonic the Hedgehog, especially during the early comics. To put it in perspective, in the future he will create the living computer NICOLE; as a kid, he grossed his friends out trying to make carbonated milk shakes.
Iron Man: Tony Stark, CEO of Stark Industries, can be a bit of an oddball.
The film version is even more so, to the point of inventing AI's that actually snark back at him.
Film
Trope Namer: Gene Wilder's portrayal of Willy Wonka in the 1971 film adaptation of Charlie and the Chocolate Factory, called "Willy Wonka and the Chocolate Factory". Wilder's trademarks in this role: ignoring others' comments because of what's Really Important right now while reciting a bit of doggerel, throwing in a pithy quote or other choice bit of sarcasm as a bonus. Also being a super genius.
Johnny Depp's portrayal is somewhat more of the extreme of this trope in 2005's Charlie and the Chocolate Factory. A genius, sure, but a genius who scares, annoys and bemuses the life out of his ex-employees, never mind his guests.
Captain Jack Sparrow (another Johnny Depp role) from Pirates of the Caribbean. A good pirate? Yes. A quick thinker? Definitely. Completely unpredictable? Foppish or odd mannerisms? Crazy ideas? Absolutely. When asked if being stranded on a desert island for months and suffering heatstroke was the reason for his... eccentricity, Mr. Gibbs rather flatly (and honestly) replies "Reason's got nothin' to do with it, mate." Sparrow's always been the way he is; a genius mix of madness,Obfuscating Insanity / Obfuscating Stupidity and Confusion Fu. Somehow, it works. Usually. Parlay?
And in his own words:
Lord Beckett: "You're mad."
Jack: "Thank goodness for that, because if I wasn't this would probably never work."
And in the words of his crew:
The captain's acting a little bit strange......er.
God from Dogma. He/She/It comes to Earth occasionally to partake in such wondrous acts as smelling flowers, playing Skee-Ball and doing handstands.
Dr. Emmett Brown from Back to the Future. He constantly comes up with weirder-by-the-minute inventions, steals plutonium from terrorists, and sets all of his clocks to run exactly 25 minutes slow. The first time Marty meets him in the past, he's wearing a metal cage mind-reading contraption on his head that puts jungle gyms to shame. Oh, and he invented Time Travel. It's a deconstruction: he has no employees and this could be why.
Edward Magorium from Mr. Magorium's Wonder Emporium. He operates by his own brand of logic, which is to be expected from a 200-year-old owner of a sentient toy store.
Literature
Willy Wonka from Charlie and the Chocolate Factory by Roald Dahl. Willy Wonka does not operate under the same rules as the rest of humanity, and will roll right past your questions without stopping. Significantly more full of wonder, less creepy, though no less mad, than Gene Wilder or (especially) Johnny Depp. This trait seems even more prominent in the sequel.
Albus Dumbledore from the Harry Potter series seems to have a mild case of this. The Hogwarts Headmaster and highly respected and able wizard seems to use a different strand of thought to the rest of the world — his unorthodox problem-solving methods and airy manner have often caused people to wonder if he's winding them up. The answer is usually no, as is shown when he gets the last laugh.
Unsurprising, seeing how his creator also wrote for Doctor Who during that period.
Discworld's Captain Carrot is this to a tee. The other characters can see some sort of sense in his optimistic, simple and innocent way of thinking, but how he can honestly, truthfully sail through events that would drive anyone else mad with a childlike smile on his face is so far beyond everyone's comprehension that most characters at least suspect that it has to be an act. Not only that, but he also has near-supernatural powers of persuasion despite very rarely using threats or violence and being shocked at the idea of blackmail, and is so literal-minded that almost any idiom or bit of sarcasm gets totally lost on him.
Mustrum Ridcully pretty much embodies this; rude and overbearing, very limited attention span and wilfully ignorant at times, but somehow seems to be an effective Arch-Chancellor
Cohen the Barbarian, as well. He takes violent exception to being called any word he doesn't know to be harmless, considers odds of 1:100,000 to be an amazing bargain, shouts terms that in anyone else would count as hate crimes, and yet he ends up as emperor of the Agatean Empire.
Danny Wallace from Join Me, Yes Man, Friends Like These, and all of his other autobiographical books, tends to act a little like this. Most of the books involve him taking on strange projects that seem unnecessary and unfeasible to those around him, but never the less make perfect sense to himself. Also the narration can sometimes take the oddest turns, and he will seem to genuinely believe something that most normal people would dismiss as impossible as soon as it occurred to them.
Psmith from P. G. Wodehouse's series. Other characters are constantly confounded by his refusal to follow a normal conversation, although he's completely reasonable in his own way.
Michael, from the Knight and Rogue Series is this. He pretty much does whatever he wants within the law and just smiles when people laugh at his odd idea of being a knight. Though he claims it took him a while to get used to this, and he does still care when dealing with his father or being treated like a retard.
Angela is definitely one of these. She is known for random quips (modeled after the author's own sister of the same name), general looniness, and concern with unusual names for already-awesome objects (e.g. a sword potentially made of diamond that can slice through anything like a hot knife through butter gets named... Tinkledeath).
Kelsier from Mistborn gathered a gang of thieves to rob the resident Physical God. And to Kill the God and take over the empire. Questions about his sanity are very commonplace.
Alexander II, King of Alaska in MaryJanice Davidson's Alaskan Royals trilogy. Fitting as the royal houshold is essentially a Cloudcuckooland.
Live Action TV
Denny Crane from Boston Legal is the definition of this trope. He shoots clients, aggressively hits on anything that moves, spouts blatant racist comments without even realising it, and repeats his full name about 20 times per episode. As he frequently points out, he's a Senior partner, and his name comes first in the practice title. Slight aversion, in that Denny's behaviour is partly down to his early stage 'Mad Cow' disease. Also, his apparent level of sanity improves when he's in court (most of the time).
Amazingly, the above description could apply to pretty much anyincarnation of the Doctor. He ranges from an archetypical Trickster to a bit of a grumpy old man, but he's always the same lovable, ineffable weirdo. Bonus points for also doubling as Inexplicably Awesome, as we really have no idea how he ended up this way.
Not to mention his logic always saves the day (after a while of alien happenings and running). For instance, in Terror of the Vervoids where the best way he can think of to combat a plant race is to accelerate their life-cycle.
Charlie Crews, the Defective Detective and Zen Survivor in Life. In the first season, his more level-headed partner is guaranteed to question his sanity and/or stare at him in total incomprehension at least once per episode. This lessens during the second season, but it's outright stated that this is because she's getting more like him, not the other way around.
On an episode of Frasier, both Crane brothers were hired to testify on opposing sides of a hearing in which a rich eccentric old man was accused of being incompetent. Frasier believed that the man was The Wonka, whereas Niles thought he was suffering from dementia. Niles was right.
Ted Allen's persona on Food Detectives on the Food Network is casually sadistic towards the cast of test subjects with a whimsical, oblivious smile; the overall effect is two parts Adam Savage and five parts highly concentrated Wonka.
Steve Valentine's persona as the host of Estate of Panic. Imagine Depp's Wonka, but 20 years older.
Judge Harry Stone from Night Court. As he points out in one episode, he might have been last on the list of people considered for becoming a judge but he was on the list nevertheless.
Jimmy James from NewsRadio, although considering how crazy the rest of the cast can be, he can sometimes be seen as just the leader of a pack of lunatics to Dave Nelson's Only Sane Man.
Music
Strange Animal by Gowan describes The Wonka as seen by a man sent to spy on him, presumably by his rivals or the government.
Henry Phillip's On the Shoulders of Freaks, a play on "On the Shoulders of Giants" with lyrics emphasizing the weird habits of great intellectuals.
Video Games
Every master in the Great House Telvanni from The Elder Scrolls III Morrowind. Even Master Aryon, who needs Turedus Talanian to bring him back to harsh reality.
Yuyuko, the Ghost Princess of the Netherworld from Touhou. She acts utterly, completely loopy to nearly everyone (save for her old friend, Yukari), treating, for example, an investigation of an incident as a midnight stroll for snacks. However, she's also one of the oldest and wisest beings in Gensokyo and is one of its major power players despite (or perhaps, because of) her unique brand of logic. This becomes apparent in the games where she's playable. While everyone is frantically investigating the cause of the latest incidents, Yuyuko tends to have already figured out the cause and the parties responsible from the very beginning; all her loopy antics are just ways of passing the time while waiting for everybody else to come to the same conclusion.
Cave Johnson from Portal 2 is absolutely crazy, and ran Aperture Science into the ground. He also founded the company.
Also from he same universe, The G-man from the Half Life series fits this. Of course, if you were to argue with him he will make your life miserable.
In Luigis Mansion, there's Dr. E. Gad, a nutty and eccentric scientist who helps Luigi.
Robert and Rosalind Lutece from Bioshock Infinite escort Booker Dewitt to the lighthouse where his mission to Columbia begins, treating the player to a Cryptic Conversation on the way and as they depart the island. They somehow end up on Columbia, and keep running into Booker to offer supplies and cryptic advice.
Web Comics
Llewellyn from Ozy And Millie. In the creator's own words, opinion is divided between those who think he's incredibly wise, and those who think he's got a screw loose. The reality, of course, is that both are true. It's just sort of a dragon thing, in general, to judge by his relatives. Their occasionally-successful dabblings in the surreal also make them a mild case of Inexplicably Awesome.
Cheese, of the Whateley Universe. One of the very few people on earth so smart that Jobe respects his intelligence. In fact, Jobe fears his intelligence, and with good reason, as seen in the short story Bad Seeds. No one even understands why he specialises so much in new kinds of lactose based technology.
Also from the Whateley Universe: Thorn. A fifteen year old mutant with the power to create literally anything from ectoplasm, who dresses and carries himself— by choice— as a Victorian era gentleman, and has an express taste for surrealistic humor.... and surrealistic behavior in general. He even looks like The Wonka, specifically the Johnny Depp version, and dresses in Victorian garb, from top hat to spats.
Dave of Civil Protection is prone to doing whatever random thing comes into his head, like pretending to be a ninja because he's bored. He does seem to be the smarter of the two main characters, though, and he knows a lot of random trivia (often about dangerous things, like how to make napalm).
The Nostalgia Critic anchors the That Guy with the Glasses organization with his insightful, poignant analysis of nostalgic popular culture. His personality, however, ranges from Man Child to violent, criminal insanity.
More than once, mental health professionals—apparently always standing by off camera in case of complete psychotic break—have intervened during reviews.
And naturally this gets deconstructed, as he's regularly depressed that his only talent seems to be riffing on cheesy nostalgia.
Goose Gladwell, a Willy Wonka parody, from the episode "Fat Man and Little Boy". Goose is a former Green Beret who fought in Vietnam and claims that his experiences from those days are what made him crazy.
The Warden of Superjail can only be described as a psychotic Willy Wonka, right down to the clothing.
King Bumi of Omashu from Avatar The Last Airbender, a man who takes great pride in being called a 'mad genius'.
Phineas from Phineas And Ferb is a child example. He even gets to dress up as Willy Wonka in the episode where he and Ferb take over a factory. (Which isn't even a chocolate factory, but hey.) Another character to be considered a Wonka in that episode was the head of the company that owns the factory. Not only did he have a chocolate river in the factory (even Phineas questioned the logic of having a chocolate river in a toy factory), but he once wore nothing but his underwear and claimed to be wearing clothes only intelligent people could see.
Professor Farnsworth in Futurama. His cloned son berates him as a total crackpot, only to later discover that the Professor's theories and inventions all work because he thinks completely outside the box.
Deconstructed in Gravity Falls with Quentin Trembley. Despite being an efficient President of the United States, his insanity got him kicked out of office. He's considered so embarrassing that there's a Government Conspiracy in place to prevent people from knowing he ever existed.
Real Life
Sir Isaac Newton. Genius? Check. Has confusing ideas that make sense the longer you think about them? He tried to reduce all of reality to basic mathematical equations, so check. Batshit insane? Check. He experimented with alchemy at a time when people had already stopped taking it seriously, and suffered from dementia caused by mercury poisoning.
He was the first person to find the reason why the orbits of the planets are ellipses, rather than circles— a problem that was a really big deal at the time. He then completely forgot about it until he offhandedly mentioned it to a friend. When his friend asked to see his proofs, he realised he'd misplaced them. Solution: rewrite all the calculations purely from memory. When the friend perused over the papers he did find, there were the whole Principia Mathematica, putting everything then known about maths, physics, optics and the Universe on its head. Newton had not organised them; it's simply that at a time, to be able to solve a problem he'd just invented infinitesimal calculus wholesale.
He poked a knitting needle into the corner of his eye, a handy gap between the eye and socket in order to test if human eyes had lenses by deforming one. Squick.
He also stared into the sun for as long as he could (something people today will always tell their kids you should not do) just to see what would happen. He was naturally blinded, but fortunately managed to recover his sight after spending days in a dark room. Guy had issues with his eyes.
Some of his eccentricity worked against his output. He was crippled by shyness, and only published his mathematical ideas at the insistence of his close friends.
Henry Cavendish made an extraordinary number of discoveries in various fields of science. He also hid from women. And like Newton, he had no desire to publish his work due to crippling shyness. Many of his significant discoveries remained unknown to the scientific world for decades after his death.
Nikola Tesla. 50% genius, 50% crackpot, 100% amazing. He was self-employed but did have to get investors.
Real Life chocolatier Louis Barnett was once considered a real-life Willy Wonka. As a kid, he was home-educated for not meeting his teachers' expectations.
Frank Zappa. The man had genius level IQ, his discography spans nearly every genre of music and features near impossible compositions. Despite his songs covered topics like fetishism, human-muffin hybrids, teenage prostitution, televangelism and even a man dressed as a House Wife courting a nuclear powered Pan-Sexual Roto-Plooker.
Billionaire Howard Hughes was no doubt a genius, and was clearly incredibly eccentric, especially late in life. (Though maybe not as much as he's often portrayed as.)
