Sherlock Holmes in Elementaryplots and nearly follows through on a revenge torture/murder and is soon rehired because he's just that good.
Dollhouse's Topher borrows a Doll to play Laser Tag in the lobby on his birthday. (Note that the Doll is a hot girl who he can program to fulfill his every desire, and he just wants to play games and talk about science fiction. The sad implication being that's the only way he'd have someone to spend his birthday with.)
His counterpart in the Washington DC Dollhouse, Bennett, isn't quite as bad, only occasionally rolling off into rambling musings. Well, that and she's psychotic and driven by vengeful rage to hurt Caroline for perceived abandonment and the permanent disabling of her left arm.
Detective Charlie Crews of NBC's Life who turned to zen Buddhist philosophy after his wrongful imprisonment. Or at least, "Zen-ish" philosophy. Imprisonment left him with a number of quirks, including a complete hatred of furniture, a love of fresh fruit and a slowness to grasp some modern-day technology (usually because it wasn't widespread before he went inside), and yet he keeps his job as a detective. It helps that he's given a certain amount of leeway because he was already wrongfully convicted.
Some of his quirks do get him into trouble. His habit of always having a knife on him is used to suggest that he is unstable and still suffering from a 'prison mentality'.
Kuryu Kohei, the protagonist of the 2001-2002 Fuji Television series Hero, is almost literally a Bunny Ears Lawyer. He constantly wears aggressively casual clothes (the entire office mistakes him for a TV repairman on his first day on the job) while his colleagues wear suits, and he indiscriminately buys random items from the shopping channel. His quirks are overlooked however, partly because he is a cunning and successful prosecutor, but mostly because his co-workers are all subtly quirky too.
In CSI: Crime Scene Investigation at least half the cast is messed up in some way or another despite being generally competent at their job, but the title definitely goes to Hodges, who is so mentally unbalanced that not only would he never be allowed to work with law enforcement in any capacity in the real world, he probably wouldn't even be allowed outdoors without some kind of supervision. (In fact he was let go for his prior job for just such reasons.)
It sort of fell by the wayside, but in the beginning of the show, it was mentioned frequently that this was the night crew. Countless other TV shows kept up a running joke that there was a night shift, rarely seen, also rarely mentioned, but when it was, it was always as an explanation for something odd that had happened; something rearranged, left behind, anything bizarre or out-of-place— it was the night shift that was responsible. Occasionally, a show would have an episode where a night crew member would join the day shift briefly, or a day shift member would work on the night crew, and usually this trope would play— the night crew member would be quirky and hard to get along with, and the day people would gripe about him, and worry that they'd end up doing his work, but in the end, he'd turn out to be brilliant, much better at his job than the whole day crew combined. Or, the night crew were a bunch of brilliant misfits, who couldn't get along with anyone else, but made a great crew of themselves. CSI was an entire series of that episode.
Before Hodges came about, Grissom held the title, avoiding his paperwork like the plague (even to the detriment of his underlings), yet he kept his position because he is made of awesome.
Coach Finstock of Teen Wolf is ambiguously crazy, competent coach and economics teacher. May or may not be talking to a team member that doesn't even exist.
Jimmy McNulty of The Wire is an alcoholic womanizer, an irresponsible Man Child, a neglectful father, and overall an asshole. However, he's also natural police, known for coming up with creative solutions for hard cases.
Denny Crane from Boston Legal. Made explicit (in a less humorous way than your usual Lampshade Hanging) in Boston Legal's more serious parent series The Practice, in which someone who'd worked with Denny assured Alan that "the plaque comes off his brain" when he's in the courtroom, and he becomes... well, Denny Crane.
Chloe O'Brian on 24. ("I was inappropriately blunt, wasn't I? I do that a lot.") By the end, she's running CTU.
The grubby-looking, abrasive, paranoid ex-spy Adam in Northern Exposure was a world-class gourmet chef.
John "The Biscuit" Cage in Ally McBeal. He was painfully shy, had facial and verbal tics (including shouting "Balls! Balls! Balls!"), routinely hung upside-down in his office like a bat to collect his thoughts, had a secret room installed in the office (the only entry to which was in a bathroom stall, by remote control), and harbored a thousand other ecentricities. Yet when he walked into court, or sat down at a conference table, and took a sip of water, everyone present knew that he was about to utterly demolish his opponent.
To a lesser extent, many of the other lawyers in the show. Ally has many brilliant legal maneuvers despite her hallucinations, Nelle is the firm's most productive associate and full of quirks involving a dreaded fear of frogs, and Mark Albert was ridiculously skilled at closing arguments, and was so obsessed with hygiene he had a dentist's chair installed in his office. Even Elaine is shown to be a genius inventor.
However, Richard is completely incompetent as a litigator; his mission is actually to destroy the law just for the fun of it, and his arguments are so over the top ridiculous that the judges groan when he starts to talk. He is, though, very good at manipulating clients into hiring the firm.
Adrian Monk's obsessive-compulsiveness sometimes throws off other characters, but it is essential to his investigative abilities (as shown on the Flowers for Algernon Syndrome episode).
He's one example of a Bunny Ears Lawyer whose weird behaviour has caused him major troubles with employment: his condition became so severely exacerbated after his wife was murdered that he's no longer allowed on the police force, and in one episode he does a compulsion that causes him to accidentally delete important police information, so the commissioner revokes the license he needs to be a private consultant.
Doctor Who: Is the Doctor in the house? Especially in his days acting as UNIT's scientific advisor... and wearing an anachronistic velvet jacket and a cape. Or a scarf long enough to touch both sides of the English Channel. Or a... whatever this is supposed to be.◊
Pretty much his behavior from day one; the First Doctor routinely abused Screw Politeness, I'm a Senior!, repeatedly tried to ditch his first companions Ian and Barbara on any planet that looked like Earth (he eventually grew fond of them) and kept flip-flopping between dangerously capable and dangerously senile.
Is House even a doctor? Like Sherlock Holmes upon whom he was modeled, Dr. Gregory House definitely qualifies as a Bunny-Ears Lawyer. He uses comatose patients for cupholders, watches sports with clinic patients, avoids seeing his own patients as long as possible, has a bedside manner akin to Lex Luthor when he finally does see them, refuses to wear a tie, plays with his gameboy/cane/ball while his patients code; and that not to mention his running commentary on Cuddy's boobs. And is a Jerk Ass every chance he gets, apparently for his own entertainment. This apparently improves his thinking processes. Lampshaded by Cuddy and Wilson in the episode Let Them Eat Cake:
Cuddy: Other doctors actually use their offices for crazy stuff like seeing patients. Not throwing a ball against the wall and calling it work.
Wilson: It's his process. That ball saves lives.
Admittedly, his coworkers tend to overlook his quirks partially because House is such a brilliant doctor, but also in large part because eccentricity is the least of his problems.
Lampshaded even earlier on when Cuddy says, word by word, He's the best damn doctor we've ever had.
House himself has more or less admitted that he wants to be a Bunny Ears Doctor, having been inspired by a brilliant Japanese doctor whose family tree makes him a virtual outcast among his own staff members.
Cuddy mentions at one point that the hospital actually has an annual budget which is basically "House is getting sued" funds, the justification being that House, while being a complete asshole loose cannon, is such a damn good doctor that the hospital doesn't really care that he apparently is threatened with legal action on a fairly regular basis. The reason? House is that damn good.
It later turns out House isn't the only one; Doctor Amber "Cutthroat-Bitch" Volakis earned her nickname soon after being introduced. She later gains insight into the fact that since she doesn't care about being liked, she has to be right all the time, or she's isn't any good to the people around her who already dislike her.
The best example on ER is Doctor Romano, who mostly just gets away with being an asshole to everybody but occassionally pulls more bizarre stunts, such as bringing in and operating on his own dog. No one dares suggest that it's inappropriate to operate on a dog and the incident is never mentioned again.
The main cast of NCIS is a ragtag lot that makes the casts of the various CSI: Crime Scene Investigations look downright normal. The most obvious case is Abby, the Perky GothLab Rat who talks to her lab machines and utterly ignores every dress code ever known to man, woman, or government bureaucracy, but the rest of the team is no less offbeat: Tony covers his considerable talents as an investigator and a leader by acting like an immature Jerk JockHandsome Lech; Ziva, the Israelite who consistently mangles her English idioms and Drives Like Crazy, started the job as a spy and assassin on loan from Mossad; Ducky talks to the corpses he autopsies (not that uncommon in Real Life) and turns every conversation into rambling stories about his Glory Days; and Gibbs seems to make it a personal mission in life to piss off anyone in authority over him... come to think of it, McGee, best selling author, computer nerd and online gamer, is the most normal member of the team.
Senior FBI agent and Gibbs's close friend Tobias Fornell sums it up neatly in the third season episode "Frame-Up" when Agent Sacks meets Tony in the interrogation room.
Agent Sacks: "[Tony Dinozzo] is implicated in a homicide and he's making jokes!" Agent Fornell: "You've never worked with NCIS before, have you, Agent Sacks?"
Most of the cast of NewsRadio fits this description: for all their quirks, Jimmy James is an excellent businessman, Bill and Catherine are great announcers, Dave is a great news director, Lisa is great reporter, Joe is a great handyman and electrician, and, despite her laziness, Beth is about as good a secretary as the insane people around her could expect. Only Matthew can be said to be legitimately incompetent at his job. (Even then he's hyper competant at his real job as a Dentist, Radio is his passion he sucks at).
Basically the core concept of Alphas. While a neurological mutation allows them amazing powers (reading EM signals, super-strength, amplified senses), it also gives them debilitating mental conditions (autism, severe temper, OCD respectively). They're technically employees of the Department of Defense, but are kept under the supervision of a psychiatrist. While they are extremely useful, "normal" people would have a hard time working side-by-side with them.
Pick a Scrubs character. Any Scrubs character. And yet, they're all excellent doctors. Except for Dr Murphy, who is merely an excellent clinical pathologist on account of accidentally killing so many patients.
The Todd probably takes the biggest slice of the cake, thanks to his constant sexual comments and idiotic behavior, but Dr. Wen once said that Todd's straightforward thought process makes him a talented surgeon. In fact, for a long time he was actually better than Turk.
Special mention has to go to Dr. Cox. His laundry list of bad behaviors all qualify, but what really tells is his antagonistic relationship with Chief-of-Medicine Dr. Kelso. Kelso even admits that, not only did he keep promoting Cox despite his bad behavior because he was the best man for the job, but that he relied on Dr. Cox's antagonism. If Cox asked Kelso for something, and Kelso said no, and Cox let it go, Kelso knew it wasn't important. If Cox kept hounding him about it, then Kelso knew it was something that needed to be addressed.
Star Trek: The Next Generation had Reginald Barclay, played by Dwight Schultz, who was shy and insecure, had a tendency to stutter, was fearful of being transported, had a holo-addiction problem, and was a hypochondriac. He also saved some lives and the ship at least once. He returned as a recurring guest character in Star Trek: Voyager: his brilliance and scientific insight led to Starfleet finding and establish transgalactic communications with Voyager, though he remained as hopelessly neurotic as ever (initially, the stress of the project and his sympathy for the stranded crew actually made him worse).
H.M. "Howlin' Mad" Murdock from The A-Team fits this trope to a T. Completely and totally mentally unbalanced, prone to assuming make-believe identities and over-personifying objects and is just flat-out loony. Who happens to be a crack military pilot.
Although there's a lot of hints that Murdock is engaged in Obfuscating Insanity when it comes to the authorities and annoying BA when with the team. And like Barclay, he's also played by Dwight Schultz. The man excels at this type of character...
The fact that it is rumored he fakes it, and can be serious without a hint of insanity (see the first season finale as an example) makes it even more awesome.
Captains Hawkeye Pierce and Trapper John McIntyre on Mash are never in uniform, chase the nurses, drink to excess, gamble, and use medical equipment to prank others. On the TV series, the early years would be filled with episodes where Generals and Colonels would appear at the 4077 and be appalled at their behavior yet refused to charge them because they were the best doctors around. Occasionally they really are Bunny Ears Surgeons, dressing in crazy outfits to make patients laugh in post-op.
From Real Life: Battlefield surgeons were often able to get away with anything short of treason because if you brought them up on charges they would be taken out of the O.R., with no guarantee of a replacement. (It goes for other medical staff, too.)
A rare example of this trope working against someone would be Klinger, who is willing to do anything to get out of the army short of shirking his duty. Unfortunately for him, that's all the army really cares about, so he never does get his discharge.
Hogan's Heroes: USAAF Sergeant Andrew J. Carter is goofy, absent-minded, prone to trip on his own feet and something of a Buttmonkey among the team. He's also their best demolition man who cheerfully subverts the Mad Bomber trope, and has the ability to become someone else entirely when in disguise—including Adolf Hitler.
Don Konkey of Dirt is a functioning schizophrenic with a tendency to skip his meds, but it doesn't stop him from being a very talented photographer, and might at times be seen as an asset, as it results in a reckless disregard for his own safety which makes him willing to go to frankly insane lengths in order to get a difficult shot. Would've gone Ax-Crazy at the end of the first season if he had listened to his hallucinations.
Biochemist Bob Melkinov of Canadian hard-scifi show Regenesis is socially awkward due to his Aspergers syndrome, but his off-the-charts IQ and wiki-like brain more than make up for it. An arc where he was considering leaving to work for a perfume company revealed that he also has an extremely well-honed sense of smell.
CSI: Miami features Alexx, The Coroner who refers to all of her corpses as "baby". A minor quirk compared to most.
John Amsterdam of New Amsterdam has lived for over 400 years, but no one on the police force he works with knows. Because, every so often, a case is solved because, say, Amsterdam knows a underground club because it was a speakeasy during Prohibition, everyone treats him like a Bunny-Ears Lawyer who thinks he's 400 years old.
Geoffrey Tennant from Slings and Arrows, who argues with his Spirit Advisor in public, stores chocolate in the skull of his predecessor, challenges one of his colleagues to a duel, habitually asks his secretary for black coffee with cream and sugar, chews on a razor blade during his rehearsals and meetings, and spends the better part of a season living in a storage closet. He's also a brilliant theatrical director.
Anna is not Geoffrey's (or anybody else's) secretary; she's the executive assistant director of the festival. She just kind of gets treated like a secretary a lot of the time.
Neatly subverted on This Is Wonderland, where no quirk is harmless. One mild example, Elliot Sacks, started out with long hair and a mildly scruffy appearance, but later went through an identity crisis that had him coming to work dressed in a different style every day. Apparently the only person who could get away with that sort of behaviour was Judge Maxwell Frasier, who wore running shoes into court, loudly complained of boredom and hunger, sang while other people were talking, and would occasionally scream.
It's just a little venting.
Sam Tyler of Life On Mars frequently looks this way to his 1973 co-workers; the real bunny ears have to be awarded to Alex Drake of Ashes to Ashes, whose firm belief that she's actually trapped inside her own subconscious causes her to be, um, less than restrained in her behaviour- as, for example, openly referring to people as "imaginary constructs," to their faces. The most prominent aversion from both these shows is Detective Gene Hunt. He's a borderline alcoholic who frequently abuses suspects and witnesses both physically and verbally. Why does he get away with it? Well, aside from the fact that he's a bloody good copper, it's also more commonly accepted in the time period.
Perhaps even moreso considering his position, Michael Scott — it's only his prodigious talent as a salesman that keeps him from being fired by Dunder Mifflin.
Let's get it out of the way: it was stolen from his Tokusou Sentai Dekaranger counterpart, yes, but the thinking position of Power Rangers S.P.D.'s Bridge Carson (namely, standing on his head) is nice and quirky. "A-Bridged" is an episode all about Bridge using his quirkiness to solve the day's crime.
That's the most normal thing Bridge does. Bridge sniffs people's dogs, wears high heels when a case calls for it, enjoys watching female cadets read from inches away, is obsessed with buttery toast, completely avoids his roommate's best frend for no apparent reason (in fairness, the friend was evil and Bridge is psychic), rambles incoherently, and is terrified of everything. Then again, he also ID'd a perp by her shoes, helped a friend rebuild an obsolete robot into armor, and manipulated a minor villain into giving up a larger villain by threatening to promote the guy's business. The latter is amazing because Bridge lacks any social graces whatsoever.
Just to emphasise this point, by the time of the 15th Anniversary Crossover, Bridge is SPD Red Ranger and field leader of the team.
Played with in Psych; Shawn Spencer's psychic abilities lead him to indulge in some fairly odd and eccentric behaviour, but almost everyone overlooks it because his visions are nearly always entirely accurate and always help solve the case... except, of course, Shawn isn'tpsychic at all; he's just highly observant, but he enjoys playing up the psychic thing, partly because it does let him get away with doing things that under other circumstances he'd be frowned on (or even arrested) for doing. Of course, he also greatly enjoys the attention as well.
Beyond the need for attention, he shows numerous Genius Ditz tendancies and held literally dozens of jobs within a few years before the start of the show, suggesting an inability to fit in normally in society. Generally speaking, his hyper-observance and ability to come up with a seemingly-insane theory in spite of blatantly obvious (usually fake) evidence allows him to pass off his act as psychic, with Gus, Jules, or his father playing the straight man to explain more mundane things to him. Bad things almost always happen when he does anything on his own.
Detective Lassiter also has elements of this, being that he fancies himself a sort of action hero and has had multiple "incidents" that has had him banned from going undercover. But he is also one of the best detectives on the force with an impressive detective exam grade.
Woody the Coronor takes Creepy Mortician and Cloud Cuckoo Lander up to eleven. He is also vital to solving many of the group's cases, sometimes finding forensic evidence even Shawn wouldn't have been able to deduce.
Walter Bishop of Fringe is released from the loony bin when events similar to the experiments that sent him there start showing up. He's still very intelligent and remembers everything about his work, but his time behind bars had some adverse effects: his first act upon being freed is to wet his pants, he obsesses over various foods he hasn't eaten since being locked up, and he constantly forgets the name or even the entire existence of another member of the team.
He also openly experiments with mind-altering drugs while on the job. His insanity is justified at one point, however, as he is literally missing parts of his brain.
Penelope Garcia of Criminal Minds talks two hundred miles an hour, plays MMORPGs at the office, gets hysterical when people interfere with her workspace, regularly answers the phone with lines like "talk dirty to me," and is accustomed to wearing elaborate hairdos and cleavagey tops (both in colors not normally found in nature) to work at the FBI. She also likes to keep a wide variety of quirky and colorful toys in her workspace. She's the resident computer supergenius.
Technically, the FBI hired her because she's one of the most dangerous hackers in the world. In "Penelope", we learn that she joined the FBI rather than go to prison.
She also has at least once worn cat ears to work. She's a cat ears hacker!
Her key skill is her ability to create search programs that sift through massive databases and correlate the information into something the agents can use to catch the killers. With a few hints she can reduce the suspect pool from millions to just dozens.
Dr. Jacob Hood, the Omnidisciplinary Scientist on Eleventh Hour. He doesn't have any one bunny ears quirk, but he does act quite oddly, melting someone's watch on a hot plate and then dipping it ice cream, entering a school building (not covertly) through the ventilation system instead of the doors, and so on. He always has some valid exploratory or demonstrative reason for doing these things, but it never occurs to him to explain before hand. Also, his eccentricities were sufficient for the FBI to assign him a handler at all times, and it has been implied that several of his previous handlers quit in exasperation.
Sons of Anarchy has an episode centered around the protection of a corrupt accountant who Knows Where The Money Is Hidden, after he completes his jail term where he developed a compulsive tic: unconscious masturbation. The character (Chuck Marstein) has his problem "cured" by a rival gang leader who amputates all but his forefingers. The Sons take him in to prevent his death, which winds up saving their season-long plan when Chuck comes through in a big way for the club in the third-season finale.
One of the Sons is a professional Elvis impersonator which seems seriously out of place in an outlaw biker gang. He is also a stone cold killer.
Lincoln Potter, the Assistent U.S. Attorney who's investigating the Sons, shows definite signs of this.
Patrick Jane of The Mentalist. He enjoys playing mind games with coworkers and suspects alike, whether or not this will actually get results towards solving the crime, and a lot of his more outrageous stunts are inadmissible as evidence. But the CBI keeps him around because he does always manage to catch the culprit.
In fact, after Lisbon's previous boss resigns, her new boss tells her outright that Patrick Jane will never get canned or prosecuted for his shenanigans. Lisbon will. Thus, it's in her best interest to keep Jane in line.
Most of the cast in JAG to some extent, but with Harmon Rabb in particular.
Basically the entire cast of The West Wing, all of them being absurdly smart and well qualified that they are forgiven a little eccentricity in how they do their jobs.
Lord John Marbury defines this trope. He is eccentric to the point of being unstable, constantly refers to Leo as "Gerald" and possesses little social grace or decorum around anyone, with the possible exception of The President and even he isn't immune. Despite this, he is a Brilliant consultant and easily one of the smartest characters on the show, possessing a very keen insight into complex issues and always acting in the best interest of Britain and America.
All of the members of Torchwood Three on Torchwood. Jack's a pansexual from the future and can't die, Toshiko's a shy technical expert who just happens to cover up murders for a living and has a horrible case of the Cartwright Curse, Ianto makes the coffee, uses a stun-gun and has a Cyberwoman hiding in the basement, Owen's an abrasive medic who is just as handy at giving bullet wounds as healing them and Gwen's an ex-policewoman who is, on occasion, just a bit too idealistic. That said, most of the time, they do a decent job of saving the planet (although it was often their fault in the first place).
Benton Fraser on Due South has conversations with his deaf wolf-dog and his father's ghost, runs around Chicago in his red serge dress uniform, and analyses evidence by licking it, among other quirks. He is, however, a very effective crimefighter.
Larry Fleinhardt from NUMB3RS is a highly eccentric scientist who, among other quirks, only eats white food, and once gave up all his possessions and spent several months in a monastery. However, since the latter came about after he got to go into space, he's clearly qualified enough to act however the hell he wants.
LAPD Deputy Chief Brenda Johnson of The Closer had her boyfriend move back out to avoid the fallout with her mom, is constantly breaking off dates to work on a case, is quite possibly the most insecure character on network television, will cheerfully lie to suspects, is generally caustic to anyone she doesn't like, and never takes no for an answer. She is also a brilliant detective who manages to close virtually every case to come her way... hence the show title. Chief Pope sums it up:
Pope: I'm sorry, she sometimes forgets there are other people. In... the world.
Pretty much all the squints on Bones are utterly brilliant but quirky. Brennan and Zack are the smartest people on the show, but extremely people dumb; Hodgins is a conspiracy theorist, and Angela is kind of a nympho. Even Booth likes to jazz up his serious FBI-ness with wacky belt buckles and crazy socks.
Agent Dale Cooper, in Twin Peaks, combines wide-eyed innocence and purity of heart with an array of highly unusual investigation techniques and an openness to the supernatural that makes Fox Mulder look like a hardened skeptic. Of course, from the other agents we see in the series, the entire FBI seems to be made up of people like this.
The X-Files' Agent Fox Mulder believes in alien abductions and every other wacky paranormal theory under the sun except the respectable ones, and refuses to shut up or censor himself to make people comfortable. He's such a joke to his peers and headache to his superiors that he is hidden away in the basement at all times. Yet he is kept around, partly because he has some powerful friends and a very competent partner covering for him, but mostly just because he is the most brilliant profiler the FBI has.
FBI Special Agent Frank Lundy is a chipper and quirky man, who does things like stopping what he's doing at one o'clock exactly every day to have lunch, spending hours looking over evidence while going through various types of music to try and find the type which will put him into the right state of mind to figure out clues, and telling his task force that he'll probably make several food-related metaphors because he "likes food". He is also a legendary investigator who has a reputation for catching serial killers in cases which were considered unsolvable, who comes just short of determining the identity of the Bay Harbour Butcher. Lundy has some quirks but it's not that prominent in general.
Dexter's colleague Vince Masuka is a very competent forensic analyst who constantly talks dirty. However, people don't tend to ignore it. They constantly complain until he cuts it and they miss his Bunny Ears Lawyer self.
River Tam from Firefly is insane and a little knife-happy at times. Half of the reason she has a bunk on the good ship Serenity is Mal's tendency toward Honor Before Reason, but the other half is because of those exceptionally useful Psychic Powers she has.
Simon's upper-class core-world behaviour is a symbol of the very people Mal and Zoe fought bitterly against during the War. Mal mainly lets him stay out of a sense of honor, but he really puts up with Simon's posh mannerisms because Simon's actually a very good doctor but still willing to serve as the ship's physician for a gang of thieves on the run.
In The Sarah Connor Chronicles, Cameron has her... quirks. Some of them being homicidal rampages. However, she's just too damn useful - being the only one among the Connors' group who can go toe-to-toe with a Terminator.
Bob Pinciotti from That '70s Show. A cheerful, dim-witted, somewhat immature man who is completely hopeless when it comes to taking care of himself, has the worst fashion sense of anyone on the show, and is given to try some strange quirks alongside his wife Midge (among them nudist and wife-swapping parties). He's also an incredible businessman, owning at least 2 establishments of his own over the course of the series and well-known to be a rather wealthy bastard throughout it. It's also worth noting that while both businesses eventually went under, it was due entirely to big businesses coming in and robbing him of all his customers with prices he couldn't hope to compete with (specifically noting that Price-Mart sold microwaves for less than the wholesale price Bob had to pay the manufacturers).
Parker from Leverage. Possibly the best thief on the planet but she has...quirks. Enough so that she spent an entire scene dressed as a nun and nobody asked her why because they figured that either it was part of a scam or her just being herself. When Nate (who has been away from the team for awhile) asks why they didn't ask for clarification- the answer was literally "It's Parker." Nate rescinded the question.
Bert Cooper, the elderly co-founder of the Sterling Cooper ad agency. He's a Japanophile who insists on having everyone remove their shoes on entering his office, fires secretaries and then forgets he did so, rhapsodizes about Ayn Rand, and congratulates employees on non-existent birthdays. But he also got where he was with a keen entrepreneurial sense, comes in to the office alone in the middle of the night to personally handle urgent business, and recognizes and rewards good work and loyalty. He also doesn't wear shoes even outside his office. He once fired a secretary because he thought she spat chewing gum onto the floor which got stuck on his socks, making him actually furious. Also, he popped in and said "Happy birthday" to Harry Crane - when they were holding a baby shower for him.
Don Draper just walks out of a business trip and disappears for about a month, somehow he holds onto both his job and his marriage (at least for another season) when he gets back. That's in addition to his regular insulting of both clients and pretty much everyone who works at Sterling Cooper — he's just so good at what he does that he gets away with it.
Subverted with Michael Ginsberg, who hadn't yet earned the right to get away with his eccentricities. Despite adoring his portfolio, Peggy almost refuses to hire him because of his total lack of professional behavior during his job interview. Don comes within a hair's breadth of firing him after he sells a company on a different, unapproved idea while thinking out loud during a client meeting — a fact which Ginsberg not only doesn't realize, but even chooses to ignore when Ken points out how angry Don was.
The Soup Nazi on Seinfeld. He treats his customers ridiculously harshly, but his soup is so good they willingly submit to his regime rather than go without it, thus his business is safe. (At least until Elaine steals his recipes.)
Don't ever call the real one a "Soup Nazi", though; he's Jewish.
A more literal example would be Frank Costanza's lawyer, whom just happens to wear a cape, and prevents a woman from jumping off of a bridge at the end of the episode.
Battlestar Galactica. Dr. Baltar is always twitching and rambling on to himself as if he's interacting with an invisible person, but no-one gives him more than a funny look because he's a recognised genius and their Cylon expert — it's not as if he has a Cylon in his head or something. A more straight-up example would be Starbuck, whose flagrant insubordination and conduct unbecoming is only tolerated because she's such a hotshot pilot.
Starbuck is a heavy drinker and has serious anger management issues, which results in her punching her executive officer on one occasion. Still, she is kept flying due to her being so damn good at it... when she's not too drunk or hung over for it.
It may help that she has strong ties with the Adama family though. And that the good commander seems to have somewhat fatherly feelings for her.
For that matter, Baltar's actual lawyer at the end of season 3, Romo Lampkin, is a kleptomaniac who wears sunglasses for almost an entire season and carries his ex-wife's cat around in a bag. He's also an amazing lawyer.
Pretty much everyone in Eureka but two people stand out in particular.
Crazy Survivalist Jim Taggart who spends most of his time hunting an apparently hyper-intelligent stray dog named Lowjack (whom he maintains is "evil-incarnate"), but is one of the best zoologists in the world.
Douglas Fargo, the man who put the Schmuck in Schmuck Bait. Though lacking in social skills and practical knowledge, as well as being a Sarah Michelle Gellar fanboy, he's proven more than once that he deserves to be in Eureka and is long established as the right-hand man of first Nathan Stark, then Allison Blake, the previous and current heads of Global Dynamics respectively.
After history is changed by them traveling to the past, Fargo finds himself the head of GD, although this is revealed to be because his grandfather, a prominent Eureka scientist in the old days, was never a Human Popsicle in this timeline and pulled strings to get Doug the position. It's the old version of Fargo who ends up turning the position into more than a Yes-Man job for the DoD. He also finds himself a girlfriend (played by Felicia Day) who's just as quirky and nerdy as him.
The doctor who delivers Phoebe's babies on Friends is obsessed with Fonzie, brings him up constantly and insists on watching Happy Days every day, even if he's delivering a baby while doing so. He's also the head of the department and delivers triplets without a hitch.
In the fourth season The Man from U.N.C.L.E. episode "The Summit-Five Affair", U.N.C.L.E.-Northeast head Harry Beldon is pretty much set up as a Bunny-Ears Lawyer. He's a flamboyant playboy who arrives at his Berlin headquarters garishly dressed, in a chauffeur-driven limousine, while drinking champagne with two beautiful women (at least one of whom is married, since Beldon tells her "remember me to your husband"). Something which is remarked on:
Illya Kuryakin: Hmmm. Harry Beldon... Everything a cautious, unobtrusive, successful secret agent shouldn't be, except he's successful.
The entire staff of Veridian Dynamics on Better Off Ted, but especially Phil and Lem who are uttery unable to function outside of a laboratory setting but are impossibly brilliant. Veronica is also a sociopath who courtship with Mordor the Unforgiving (not Kevin!) involved things like slaughtering a goat.
The Big Bang Theory: averted by Sheldon Cooper. Despite being allegedly of the most brilliant scientific minds on the planet, he gets fired, is not asked to return (nor is hired by anyone else) and only manages to get his job back because his mother seduced his boss. Most telling, the people he calls friends can barely stand him and usually only go along with his plans because they'd literally never hear the end of it from him. He's constantly having to defend his behavior to his boss, and usually ends having to back down because he knows his boss will be all too happy to fire him again.
Judge Stone from Night Court. Ironically enough, with all his wacky co-workers & clientele, he often comes off as the Only Sane Man, despite his own undeniable quirks.
Glee's Brittany Pierce is dumber than a jar of mayonnaise, "thinks the square root of four is rainbows", once took cold medicine and forgot how to leave a room, and still believes in Santa Claus . . . but get the girl on a dance floor and prepare to be blown away. She also has a peerless knowledge of feline illnesses, earning her a spot on the school's Academic Decathlon team.
Also, this trope in combination with desperation is the reason why they let Kurt join the football team, even though he's Camp Gay, hated and bullied by the football team and almost everyone else, and can't do it unless he gets to listen to his music meanwhile. The team has had bad enough of a year that, when Kurt shows up, claiming to be auditioning for the role of kicker and actually pulls it off, the coach is more than happy to have him on the team.
Coach Tanaka: Can you do that, with the game on the line and ten gorillas bearing down on you, wanting nothing more than to taste your sweet virgin blood?"
Kurt: Sounds like fun. Can I have my music?
Coach Tanaka: If you kick like that you can wear a tutu for all I care!
Which really doesn't make sense to anyone who knows anything about football. He may be an accurate kicker, but the time it takes him to do it with the music should allow any opponent to block his kicks. All the other schools in the district must be terrible on special teams.
Sue Sylvester may also qualify; she's Crazy Awesome and possibly Ax-Crazy as well under the right circumstances, but she genuinely is a world-class champion cheerleading coach who brings in Nationals tropies by the bucketload - and funding to her cash-strapped school - so she's generally allowed to go her length. Generally.
Dr. Cal Lightman on Lie to Me. He sticks his nose into his team's personal business on a regular basis without hesitation, he acts like a Jerk Ass to everyone (clients included), and has a fairly big ego. He's also brilliant at what he does. He never seems to miss a single flinch, even on random passerbys.
Detective Dan Stark from The Good Guys is a fantastic 1981 cop turned Bunny-Ears Lawyer due to not progressing with the times. Despite this, he still proves himself a fantastic, if unorthodox cop, uncovering and solving major crimes while handling minor ones. He even once managed to cuff himself to the pimp/murderer while being choked out from behind.
Dr. Kylie Johnson on MADtv is a 19-year-old doctor who would often never take her job seriously, doing things like wear belly shirts or play practical jokes. However, she is among the best in the medical field.
A poker player in Black Books is nick-named "mouse ears", and does in fact, wear huge novelty mouse ears while playing. One of the other players is apparently deaf and blind, but can still apparently play poker quite well.
Doctor Martin Ellingham in Doc Martin is abrasive and arrogant, and generally unsociable. He had also developed a blood phobia, which caused him to have to give up his prestigious surgical practice and become the best damned GP (general practitioner) the village of Portwenn ever had.
Ari Gold from Entourage. He yells racist homophobic sexist or just degrading insults to pretty much everyone but still (almost) always gets his way. Maybe averted in the end of Season 7.
Holly from The Exes is an almost literal example as a divorce attorney.
Law & Order: UK has defense counsel Jason Peters, an obsessive-compulsive germophobe who's never lost a case.
The closest comparison to Jason Peters from the original Law & Order is Randall J. Dworken. He makes Jack work hard through a liberal use of tapdancing and oafish charm. Dworken is introduced by objecting to 'the people of the state of New York vs. his client' because he is certain that the twelve jurors seem reasonable people.
Detective Zack Nichols from Law & Order: Criminal Intent is described as this (although not in so many words) by Captain Ross in his debut episode. As is typical of Jeff Goldblum characters, everything about him is a little bit off, and he once left the force for seven years to discover the meaning of life. Goren seems like he should be this, but his offputting quirks appear to make him a more effective interrogator, which puts him closer to Crazy Awesome.
Judge Mike "The Hammer" Reardon from Justified. Man wears little more than a Speedo — and shoulder-holstered .38 — under his judicial robes, and spends his off hours in hot pursuit of hard liquor and loose women. But once court is in session, he's a Hanging Judge who regularly throws, not just the book, but the entire damn Lexington (KY) Public Library, at the guilty.
Supernatural has Dean, he of the frequent hitting-on girls, affection for junk food, and daddy issues, and Sam, Dean's brother, who has daddy issues, mommy issues, and isn't exactly the most delicate under the covers. They hunt monsters and pal around with an angel with his own set of quirks. The upper echelons of angels and the King of Hell are scared of them.
Crowley: Am I the only one who doesn't underestimate those denim-wrapped nightmares?!
In fact, just about every main or recurring on the show has their own set of traits; even Death has an odd affection for cheap food.
Dorothy in Golden Girls once dated a lawyer who wanted to retire from law and become a circus clown. He was very serious about this. When the Girls got in trouble over an environmental protest, the lawyer comes to their rescue — wearing part of his clown costume.
Dr. Geiger from Chicago Hope had some quirky habits of playing music in the operating room, dealing with stress by taking off his pants and playing with trains in his office, and just generally being a strange person who was not very easy to get along with. But he was also a brilliant heart surgeon, so people were willing to put up with it.
Necessary Roughness centers on a therapist who helps professional athletes and other celebreties whose quirks have started to affect their job to the point that they cannot get away with it anymore. Often enough they have serious problems that were overlooked specificly because they were so good at their profession that people just accepted them as eccentrics and did not seek help for them.
Kougami from Kamen Rider OOO. He's a Large Ham who has an obcession with birthdays and seems to spend more of his time baking cakes than running his massive company...and yet is a heroicChessmaster and Manipulative Bastard who managed to Out Gambit a living embodiment of human Greeed and is pretty much the Big Good of the series. His company has invented hundreds of devices that help the heroes out in the battle with the Greeed and he pretty much knows everything about the Greeed and the events of 800 years ago.
Shotaro Hidari from Kamen Rider Double the year before also counts; he's apparently obsessed with living the 'hard-boiled' '50s noir way, yet is good enough as a private investigator that his Friend on the Force lets him have full leeway with every case.
Implied with Frasier and Niles Crane from Frasier: they're both ridiculously neurotic, eccentric, and have personal lives so screwed-up and behavioral tics so shocking that if you'd never met them, you'd wonder why anyone would consent to get therapy from such colorful characters (Frasier, among other breakdowns, once spent several hours on a ledge above Cheers threatening to kill himself after his wife left him, while ranting about her affair at the crowd below; while Niles once had a Heroic BSOD and stripped stark naked in the middle of Cafe Nervosa after enduring several sleepless nights of constant media hounding and Disaster Dominoes when his ex-wife was arrested for a sensational homicide). The answer, of course, is that they're both absolutely brilliant psychiatrists (and they demonstrate it in nearly every episode too — it's not an Informed Ability), mentioned to be among the best in the American northwest, enough to retain their respected standing in Seattle's high society despite their general insanity.
The civilian crew of Primeval. As Lester explained to Becker:
Lester: You will be dealing with a highly strung and temperamental team of rank amateurs who just happen to be brilliant at what they do.
Jeff & Lester of Chuck are stated by the title character to be better than the CIA's best computer experts, if they're focused. The kicker? Lester's a somewhat sociopathic egomaniac, and Jeff (At least for the first four seasons, before recovering from carbon monoxide poisoning) is the show's resident Cloudcuckoolander.
Chuck himself qualifies too, but in his spy career, not his computer repair career. The Intersect gave him encyclopedic knowledge of espionage and international conflict, and the Intersect 2.0 gave him basically any skill that could be useful to a spy in short bursts (such as marksmanship and almost every martial art and language). He'd be a perfect Tuxedo and Martini spy if not for being a Technical Pacifist and very socially awkward.
Dr. Mark Sloan in Diagnosis: Murder occasionally made his rounds on rollerskates, made latex gloves into balloons, seemed to take pleasure in driving hospital administrator Norman Briggs into apoplexy and generally acted, well, like a character played by Dick Van Dyke. He's also a brilliant surgeon and diagnostician, and frequent consultant to the police department.
Richard Castle is a bestselling writer who helps a homicide squad out with their investigations. One of the things he brings to the table is Connections. Another is money to throw at certain problems, including buying a high-end cappuccino machine. The third, and most important, would be his unusual perspective on the cases, compared to the three cops. He comes up with crazy theories all the time, and they are occasionally proved right. One scene had him explaining his latest wacky idea to Beckett, then instead of rejecting him, she admits she can't come up with anything better.
Colonel John Sheppard of Stargate Atlantis, for the most part, is a laid-back guy who would rather play with all the cool toys and enjoy the perks of being in another galaxy. He's also an Ace PilotColonel Badass who can kick forty different kinds of ass when the safety and lives of Atlantis come under fire, often proving why the position of the military commander of Atlantis rightfully belongs to him.
Jack O'Neill of Stargate SG-1 basically paved the way for Sheppard, as Jack's fought off multiple invasions of Earth from the Go'auld and still finds the time for a fishing trip.
Worth mentioning: Richard Dean Anderson once asked General John Jumper, then-Chief of Staff of the Air Force, if he had colonels as bunny-eared as O'Neill. Jumper replied that he had colonels who are worse.
Rodney McKay of Atlantis fits into this trope as well. He's a raging egomaniac with a hair-trigger temper and a tendency toward hypochondria, but he just so happens to save the day virtually every time, so he's considered one of the most valuable members of the team. Not only that, but as the show progressed, he became more of a "main character" than many of the other "main characters", with quite a few more episodes focusing on him than on them.
Merlin plays with the trope. Merlin is a horrible servant, his primary job, but his secondary job, providing support for Arthur, is so good that Arthur can't bear to fire him despite the fact that Arthur thinks he's a complete Cloudcuckoolander. Further played with because, while no one knows it, Merlin is an extremely badass and smart self-appointed Court Mage, and has saved Camelot and Arthur multiple times without anyone knowing.
Doesn't really fit the trope. Merlin's second "job," as you call it, is nowhere on his contract — that's just him being a good friend, and Arthur keeps him around because they're Heterosexual Life-Partners. A better example to fit this trope would be Gwaine: he's impulsive, The Alcoholic, the Butt Monkey, an outrageous flirt and, prior to becoming a knight, was constantly on the run from some angry unpaid bar-owner or another — but with his loyalty to his True Companions and his swordsmanship, Arthur'd be a fool not to include him in the Knights of the Round Table.
Franklin & Bash: Lawyer Peter Bash has not worn bunny ears, but he has dressed in a Kangaroo character costume (while smoking a fake joint) to win a tort case. In fact, this trope is the overall basis of the series.
Peter Lattimer from Warehouse 13 is a manchild and not very book smart compared to the people he works with, but he has good crime-solving instincts, is physically fit and even has low level psychic ability.
Diego Soto from Alcatraz has a case of arrested development and had no aspirations beyond running a comic book store until he was drafted to help track down the "63s". This is despite being a genius with PhDs in Criminal Justice and Civil War History in addition to being the world's foremost authority on Alcatraz.
The Stonewall Jackson sketch from Horrible Histories is a succinct demonstration of this trope in action: quirks displayed, disbelief from the newbie, and competency proved.
Spencer from iCarly is an almost literal example. He spent only three days in law school, but in "iPromote Techfoots", he put what he learned in those three days to good use.
Will Graham from Hannibal is a Bunny Ears Profiler thanks to his abnormal empathy. Subverted in that it doesn't make him particularly quirky or cheerful or even liked, but rather more like he's on the brink of going insane.
While attention isn't brought to the matter, fans have noticed that in Once Upon a Time Regina continues to work as mayor after the curse is broken, using her old office and even doing paperwork. That's right. The Evil Queen who cursed everyone still runs the place. A fan asked if the good guys sucked so much at being in charge that she just took over again, and the creator replied "Pretty much."
Dr. Theodore Morris from CBS's Now and Again. He has a tendency to randomly break out into song, has been known to growl at people who annoy him, and when he's smitten with a woman the normally erudite Theo literally cannot construct a proper sentence. He's allowed mostly free reign over his project because he's so brilliant, though; he literally created a new body for Michael with extraordinary abilities, and even outside of his classified work he's lauded as the founder of the "human construction sciences" movement.
In Season 4 of The Voice, it's revealed that, as a coach, Usher has some very... eccentric... ways to train his singers to be better. The best example might be when he gave singer Michelle Chamuel instructions to drop and do push ups, then jump up and start singing, as a means to increase her breath control. Also, he gave Chamuel the Cyndi Lauper classic "True Colors" (a song about never giving up and believing in yourself) for use in a Knockout round performance, and during rehearsals instructed her to sing the song to herself in a mirror, as a way to get her to get her to open up to the audience more. It worked.
Likewise, Blake Shelton taking his team of would-be country singers to a Karaoke Bar, where they sang everything but country, was a means to get them to realize that the most important part of being a performing musician is loving the music itself and having fun with it. This also worked.
Floki from Vikings generally comes off as a crazy madman, though probably the harmless variety. However, he's a brilliant shipbuilder, a skilled healer... and he is anything but harmless.
Harper from Wizards of Waverly Place is intelligent enough that cribbing off her and getting her to do her homework is one of the reasons Alex hangs with her but she is decidedly odd, especially when it comes to fashion choices. Although, in "Dollhouse", her ability to paint incredibly small things precisely (due to her fashion design skill - those are some very strange outfits) helps Justin make a nice chunk of change.
Vince Noir of The Mighty Boosh is an air-headed Camp Bi weirdo obsessed with fashion, fame and Gary Numan. He has no qualifications for working with a zoo, he dropped out of school, he dresses up animals as pop stars and the owner of the zoo he works at hates him to the point of trying to kill him more than once, but he's always allowed back because he has the magical ability to talk to animals and thus understands their needs better than any of the trained keepers.
David Creegan in the U.S. version of Touching Evil. After suffering from a bullet to the head, Creegan is literally missing parts of his brain; specifically those that regulate shame. Aside from that (and seizures, and order recognition issues), he's still a brilliant profiler and the place he gets hired at, the Organized and Serial Crimes Unit, he actually helped to found before he was shot. Hilariously, after about the first two episodes, despite the fact that he is the bunniest ear'ed lawyer of all, (rolling cartwheels in the middle of conversations, playing hangman in the middle of a case involving a serial killer who is called the Hangman, hugging people, laying down in the middle of the table while there's a group meeting going on, stripping and shouting in the middle of a flight, interviewing suspects for less than a minute and sending them home, playing with signs and setups, and has an acute schizophrenic as a roommate and generally acting like a two year old in a thirty year old man's body), his behavior is almost never explained to newcomers or people that they're interviewing and is hardly mentioned in the office except when it comes to his clothing. (Occasionally, Creegan will say "I have this thing" and points to his head and doesn't explain anymore than than that.) For the most part, his partner, Susan Branca (and the rest of the OSC) just rolls with his weirdness and she actually starts picking up a few bad habits of her own. Branca even uses it to her benefit ("Tell us what you know and I will totally take him home.") and more often than not, because she doesn't mention it, Creegan actually makes an effort to self-regulate around her as best he can. Don't think that she's a pushover, though, any time Creegan mentions a physical symptom, Branca is quick to go over what his limits and problems are, citing that they have a dangerous job and they need to be clear on his issues. Could be justified in the fact that as profilers, they know that traumatic brain injuries don't actually have a cure and David actually can't control himself because it's biological and not behavioral.
Ed Wachtel in Hill Street Blues is a lawyer who later becomes a judge. At the advice of his psychiatrist, he wears not bunny ears, but a dress in court, which causes a few raised eyebrows but no serious repercussions.
Elsbeth Tascioni of The Good Wife is so flat-out wacky that if you took away all her quirks, there'd be nothing left but a law book.
Jeff in Community is shown to be one in flashbacks, as though he didn't possess an undergraduate degree and came up with the most ridiculous defenses, he never lost a case.