The Mayor of Steelport is often stated to be the only person capable of keeping a city of rampant gang violence, homicidal maniacs running wild and hosting game shows, and general insanity functioning with any kind of stability or sanity. He is also Burt Reynolds, and still loves going out and solving violent disputes personally.
Kinzie Kensington is a paranoid conspiracy theorist whose sexual proclivities frighten even the Boss. She is also a brilliant hacker who can give Matt Miller, leader of a gang of cybercriminals known as the Deckers, a run for his money.
Miller himself is no slouch when it comes to hacking. He's also a goth and a massive Nyte Blayde fanboy.
The Boss falls into this a lot, but never more so than in Saints Row IV. Whether it's singing along to the radio on the way to a fight, pretending to shoot things with a sniper rifle while on lookout duty, installing stripper poles in the renamed White Crib, proclaiming yourself "the patron saint of America" (even if the accent you use is French or Cockney), blowing up statues of the bad guy just out of spite, doing a striptease routine at the most ridiculous possible moment or bestowing all rights to the Nyte Blayde franchise to a teammate after fighting through their dubious-quality fanfiction, you get up to some fairly ridiculous stuff, but at the same time you prevent nuclear disaster by climbing up a missile in flight, parlay that into becoming the President of the United States, and then bring an interstellar empire to its knees through an unequalled gift for killing stuff.
Since Ghost Trick has the same developer as the Ace Attorney games, it's expected that it also has a few bunny ears. Inspector Cabanela stands out as a special investigator with a spotless record and intense ambition to climb his way to the top. He also dances everywhere he goes, including up and down the stairs.
Checky, the Resistance Job Instructor for the Mechanic path, is a guy in a mascot costume as his civilian self. As one of the leaders of the Resistance, however, he continues to wear the costume head. All the time. Even while sleeping, or piloting a Mini-Mecha tank against a global organization trying to resurrect the Black Mage. He also wears a second costume, under his 'civilian' costume.
Hersha, the Cygnus Knights' correspondent in Ellinia, is described as a very good informant, who is also paranoid about everything. You can undertake a quest from him where he demands that you attack local monkeys and confiscate their bananas, because he's convinced they're bombs. He does, however, prove to be a reliable, thorough researcher in the Cygnus Knights' questline.
The leading lady of Sakura Wars: So Long, My Love, Gemini Sunrise, is a southern belle who is absolutely enamored with Japanese culture and has a tendency to get lost in her own head. She's also a highly-skilled swordswoman and one of the most talented members of the New York Combat Revue.
All the robots in Haven count, One-Eye especially. The whole reason they have more personality than the Mecha-Mooks is due to slight malfunctioning, making them a bit nutty. Still, they're essential in helping your character infiltrate the Black Heaven, and later can produce some of the best armor and weapons in the game.
Excellen Browning is a goofy, flirtatious woman who insists upon being called "Big Sister" rather than "Ensign", and has on more than one occasion donned a Playboy Bunny-style costume to raise her teammates' morale. She also happens to be an exceptional mecha pilot and an insanely good sniper, as well as part of one of the most respected and feared teams in the SRW universe.
The only OG character who doesn't have shades of this is Russel Bagman, who's easily the most "Normal" member of the team. Ironically, this makes him stand out to many fans.
During his introduction in scenario 5 of Shin Super Robot Wars, Ryusei quickly establishes himself as some kind of crazed super robot otaku, and Prof. Hamaguchi confides to Akira that as a pilot, Ryusei is first rate.
There's also a subversion or inversion of Crazy Awesome going on here as well, as the game is set on an Indian Burial Ground stated to mentally destabilize everybody in its vicinity. The sufficiently curious will discover that all of the kids (including the protagonist) have serious problems (many aren't far from homicidal or suicidal behavior), and that the adults may even have accumulated more (over their longer lives). Their competence, power, and control are the reason why they're Bunny Ears Lawyers: the available alternatives are far worse. As demonstrated by the game's plot.
Jody Crawford of Metal Wolf Chaos enjoys watching soldiers getting slaughtered by her boss's Humongous Mecha a little too much, and apparently spends her spare time wondering about how various buildings would look if they were destroyed, and somehow managed to become secretary to the President of the United States. Although considering what President Michael Wilson gets up to, Jodie probably looks like an icon of sanity by comparison.
Hal Emmerich is both a brilliant engineer capable of designing a functional bipedal tank and enough of an Otaku to program the weapon's movements based on Street Fighter. In Metal Gear Solid he's so essential to making Metal Gear REX actually function that the Quirky Miniboss Squad have to keep him alive and programming even after disposing of the rest of the development team.
Ocelot is a ridiculously superb marksman and the series' resident Magnificent Bastard who is also unhealthily obsessed with his revolvers and Big Boss.
Even Snake himself, a formidable warrior by anyone's assessment, has his tendency for meaningless philosophical ramblings and a rather disturbing relationship with The Box(TM). It's also implied he loves trashy action movies and women's figure skating, he's a fan of dog-sledding, and one of the Japanese-only supplemental material guides revealed that his favourite food is blueberries.
Empress Sanaki of the Fire Emblem Tellius games is a Bunny Ears Royal. In Path of Radiance, most of her early interactions with the protagonists involve her jerking them around and forcing them to learn for themselves what's going on instead of just telling them what's up simply because she was bored. Three years later in the sequel, we see her commandeering the King of Kilvas to carry her onto the battlefield because she couldn't bear not knowing what was going on, then later learns that he's bound by a blood pact to the Begnion Senate—and that she can essentially free him from their control since her orders carry more weight than theirs do. And of course, when one of her most trusted aides turns out to be, well, not exactlyevil but still responsible for all of the bad stuff that happened, she decides that his punishment is to be drowned in rancid butter.
The brilliant engineer Dr. Cid from Final Fantasy XII fits this trope well—the Draklor Laboratory and the Archadian Empire as a whole manage to ignore his conversations with a not-so imaginary friend due to his skill at manufacturing airships and weapons with nethicite. Balthier, however, was not quite so tolerant.
The Dungeon Master noble in Dwarf Fortress is a talented animal trainer and metalsmith who permits your fortress to train a variety of creatures you usually can't. He or she tends to also wander around the fortress, naked except for a cloak, shoes, and gloves.
The doctors in Rayman 3: Hoodlum Havoc. They're recommended as exceptionally good doctors, and are shown to be at least reasonably competant, but their behaviour is decidedly odd, and their methods even more so.
All the teachers of Persona 3 that the protagonist has as his personal teachers seem to be this. There's Ms. Isako Toriumi, the homeroom teacher with an almost "L"-like addiction to sweets (especially cake) and to playing MMORPGs as a l33t-speaking alter ego, in which guise she grants the Hermit social link and even forms a crush on the player. There's Mr. Edogawa, the school nurse with his over-the-top obsession with mysticism that causes him to insist on making the player drink useless potions for treating ailments and who derails any class he subs for by giving lectures on magic. There's Mr. Edo, the history teacher who always wears his Sengoku-era samurai helmet and geeks out about samurai all the time — like constantly complaining about having to teach history prior to the Sengoku-era, because there's no samurai to talk about. And then there's Ms. Miyahara, the math teacher who spends most of the class just gushing about the aesthetic beauty of numbers. They're all shown as very knowledgeable, and they're all various shades of Cloudcuckoolander.
In Persona 4, though, there's only two such kooky teachers, and they are far less bizarre. An older gentleman who likes to teach with a little hand puppet of himself, and a female history teacher, Ms. Sofue, who always wears an Egyptian pharaoh's headdress and carries a ceremonial crook. She's actually the sister of Mr. Edo from Gekkoukan High School above, though unlike him she has a love of history in general instead of being fixated on one era, and so she carries out her lessons with general enthusiasm.
Persona 5 brings us Tae Takemi, who runs a back alley clinic in Tokyo, dresses like a goth, and has a very morbid sense of humor. In spite of these idiosyncrasies, she is actually one of the most brilliant doctors in the country, and as you forge a bond with her, she'll provide you access to her own homemade medicine, all of which are very beneficial during your ventures into the Metaverse.
It is strongly implied that a light-side Knights of the Old Republic or Knights of the Old Republic 2 PC tolerates HK-47's Ax-Crazy discourse because he is the only thing that can translate the Tusken tongue and a rather capable warrior
Minsc. He's quite nuts, but when he talks about kicking butt, he knows what he's talking about.
Dynaheir: Minsc is, well, Minsc, but he hath a strong sword arm.
Also, none of the mages are exactly well-adjusted, with the possible exception of aforementioned Dynaheir. And even she speaks funny.
Kivan is also pretty quirky: he's reclusive and has attitude issues. But Kivan is also God and the game cannot be won to any kind of satisfaction without him. He's by far the best archer in the first game and his THACO defies all reason.
In Final Fantasy XIV, Godbert Manderville is a highly eccentric old man who dresses in a tuxedo with short-shorts (if even that). He is also the best goldsmith in all of Eorzea, using his considerable skills to amass a fortune that earned him a seat in Ul'dah's Syndicate and allowed him to open a highly successful entertainment establishment.
Thane seems overly contemplative for an assassin, but we learn that he has been recently diagnosed with a terminal disease, Miranda is pretty normal for a member of a shady organization aside from the Designer Baby Blues, Samara is a Scary DogmaticBlue Skinned Space Babe, Grunt is a Designer BabyProud Warrior Race Guy, and Garrus is a level-minded realist (quite possibly the most level-headed of all characters despite some issues in his past, and one of the only ones who literally never loses his cool). This leaves Jack and Mordin. The latter however takes this trope to its full extent.
Jack is an uber-powerful biotic who subjects anyone she meets either to a biotic blast or a Cluster F-Bomb. She mellows out as the story plays out and, by Mass Effect 3, is slightly more level-headed and even makes a great effort to avoid swearing (unless you happen to be Joker, also an example of this trope). Mordin is a brilliant scientist with a Motor Mouth and love for "Gilbert and Sullivan". By the third game, he's close to 40 (making him an old man by salarian standards) and thinks of retiring to a house on a beach. When Shepard points out that he'd get bored collecting seashells all day, Mordin points out that he'll run tests on the seashells. He then goes out with a bang while singing.
Jeff "Joker" Moreau, as his nickname implies, is constantly cracking jokes and is rarely serious about anything. He also has brittle bone disease, making him physically unfit for military duty, technically speaking. He is also the best frigate pilot in the Systems Alliance, and no one who has seen him in action is going to dispute that claim.
Mass Effect 3 gives us Javik, who is a rude, selfish, arrogant tool who is profoundly bigoted against synthetics and describes everyone around him as "primitives". He's also the last Prothean, has keen awareness of Reaper strategy, and is a potent biotic on top of that. The Citadel DLC also adds Brooks, who is largely clueless about action away from her desk, names a security program after her cat, gets really giddy after a medi-gel overdose, and is still the only person with the right blend of tech skills and low-tech equipment to be able to infiltrate Elijah Khan's casino...until it turns out that she's been putting on an act all along, and is in fact a very competent villain who's been playing you the whole time.
The World Ends with You gives us Sho Minamimoto. A Mad Mathematician, who always speaks in mathematical terms, makes junk heaps he calls 'art', and is very egotistical. However, he's one of the youngest Reaper Officers to become a Game Master, and excels in all areas of leadership - except cooperation. He's also one of the toughest buggers to beat in the game. The Secret Reports reveal that he was working with a Fallen Angel, who picked him precisely because of this — since everything Sho does is unusual, no unusual behavior prompted by the Fallen Angel would be worth investigating further.
As first shown in "Meet the Pyro", the Pyro is a BEL among BELs. S/he's not at all in touch with the real world, which s/he imagines to be a Sugar Bowl, even when causing death and destruction. When s/he's burning things, s/he's spreading bubbles, flowers, and magic. When s/he splits an enemy's head open with an axe, s/he's feeding them a lollipop; when using his/her flare gun, s/he's blowing bubbles. S/he also sees his/her enemies as chubby cherubs, wings and all, which prompts his/her "kindness". You also get a promotional "Pyro's goggles" that let you see the world as s/he does. Everybody is laughing even as they get shot, blood is replaced with random items such as gears or balloons, and fire with sparkly rainbows and happiness. To top it all off, you don't get "dominated" and get "revenge", they "become best friends" and "break up". However, as any player will tell you, if you are close to him/her, expect to be dead soon. Very, very soon.
Agent Francis York Morgan ("Call me York. That's what everyone calls me") is an FBI investigator who we first see driving a car while working on his laptop and arguing on the phone with his superiors over inter-dependence issues in Tom and Jerry. He is also routinely late for appointments, rambles on endlessly about old movies and their directors when he's not cheerfully discussing grisly murders and serial rapists over dinner, and goes over his every action and decision with his imaginary friend, Zach. His methods of "investigating" consist less of actual forensic work and more of chain-smoking until he gains visions of the past, and seeing visions of the future in the milk he pours in his coffee every morning. Despite all this, he's an extremely competent detective who isn't at all shy over that fact.
Infinite Space has a few, but Lord Roth and Thomas Veil stand out the most. Lord Roth is a rather childish man who enjoys his Chick Magnet status a little too much (and puts his aide, Nele, into a lot of troubles because of his quirks), yet he is one of Regeinland's top commanders. Meanwhile, Thomas is an agent of Federation Security Network directed by Brad Lennox and a good crew member for your navigational post, who happens to be a fan of young Idol Singers, almost to the point of being a creep.
Demon Prince Laharl from Disgaea is the heir to the throne of Netherworld, and he got some strange ideas as to what a King should do: If money is needed, it’s time to loot some noble’s mansion. Assassin love angels are potential recruits. Laughing evilly on a regular basis is a requirement. Ideal Overlord tasks are making it rain pepper so that the humans will sneeze their nostrils out or deprive children of their sleep by giving them addictive video games. Heroes should not just be defeated; enslavement is the way to go. But he is very passionate and dutiful about the job, not to mention extremely powerful, so he gets it and does a good job all things considered. His vassel Etna has not dethroned him...yet.
Laharl's entire command structure. Etna is a Jerkass and is openly contemptuous of his authority, Flonne is obsessed with LOVE and TV, Sicily literally tried to overthrow him, but all of them are reliable-ish, skilled, and - although he'd eat hot coals rather than admit it - his friends, so he hauls them around with him anyway.
Nero from Devil May Cry 4. Much of his Jerkass attitude would've gotten him excommunicated from the Order a long time ago, such as a blue coat instead of their white uniform (although he does have their insgnia stitched on it), listening to his own theme song during prayer, and colorful mouth. However, he's very good at his job in the "dirtier" side of things, and is kosher with the idea of God (in fact, he out right states it near the end of the game) - he's just not all that fond of the church he works for.
The Secret World has the leader of the ultra-capitalist Illuminati, The Pyramidion. He speaks in a calm, evenly-paced tone, and clearly knows everything worth knowing. He just has this peculiar habit of peppering his dialogue with odd Public Announcements and context-relevant memes...
Makoto may act like a big kid, but she's an Intelligence operative and quite a talented one at that.
Kagura from Chrono Phantasma. He's every bit as badass as you'd expect the head of the top Duodecim family to be, despite the fact his personality seems to be continually stuck between a Fratbro and a potential sex offender.
Emperor Peony IX of Malkuth in Tales of the Abyss is by far the most competent and effective monarch in the story, not to mention about the only person who can get the better of Jade in a conversation. He also keeps his five pet pigs loose in his bedroom, and likes forcing the main characters into different outfits so much that he's responsible for no less than nineteencostume titles.note Six swimsuits, six final battle outfits, seven Power Rangersexpy cosplays, and Jade's Battle Master costume, minus one because the swimsuit he picked for Tear was apparently so embarrassing she refused to wear it.
Raven from Tales of Vesperia. A "fishy old man" who acts lazy, flirts with the ladies, and apparently likes sleeping on the beds in jail, finding them comfortable. Not only is he a right hand man of Don Whitehouse, a super competent warrior and commander, but he's also Captain Schwann, a highly respected and powerful knight captain in the Imperial Knights.
Most of the henchmen you recruit in Evil Genius tend to start at "kooky" and go very strange places from there, and usually axe-related places at that, but they also bring skills that utterly humiliate the minions you start out surrounded by.
Mimi Meers in Pocket Stables technically wear bunny ears. She also starts off with very well balanced and decent stats.
Merrill is another example; she's a ditz girl who gets ridiculously lost whenever she goes out into the city on her own and tends to get sidetracked by daydreaming about things like having a baby griffon as a pet (ignoring the fact that griffons are believed to have gone extinct centuries ago). She's also a terrifyingly powerful Black Magician Girl.
Dekar in the Lufia series hails himself as the world's strongest warrior, and proves an excellent soldier as well as a faithful protector and advisor to Bound Kingdom's prince. He's also a shameless flirt and immensely stupid, to the point where he's unable to remember how to leave a room he had just entered. He'd be Too Dumb to Live if he wasn't every bit as good a fighter as he says he is.
Barnaby "Screwloose" of Armello doesn't entirely seem to understand what's going on around him, or that he's in the middle of a fight for the throne... but he's still a talented warrior and adventurer, able to compete for the crown on weight of that alone. (His literal bunny ears are a bonus.)
All the Goddess CPUs in the Neptunia series. Neptune is The Slacker par excellence, Noire is highly efficient but socially clumsy and neurotic, Blanc enjoy writing trashy fiction and has a staggering temper, and Vert is an online gaming addict and a Yaoi Fangirl. Their sisters? Nepgear is easily flustered and gets distracted by machines, Uni is a military otaku with an inferiority complex next to her sister, and Rom and Ram are children. It's joked the nations could do a better job taking care of themselves... and in Megadimension Neptunia VII, we see that happen. The world falls apart, due to Gold Third's inept leadership. C-Sha tried to gently guide Lowee from the shadows, but instead let a corrupt man seize power an institutionalize a dystopian license system to quash dissent and stop social mobility. K-Sha outright ran away from ruling Lastation and allowed a corrupt mercenary group to seize power and take the nation on the warpath. S-Sha is holding Leanbox together only because she needs its resources to meet her personal goals and her short-sighted policies are causing looming problems. Only Planeptune continues more or less the same, because Histoire still has authority and B-Sha is Not So Different from Neptune, although the former is afraid with monsters. As eclectic as they are, the Console Patron Units hold power by more virtue than simply being Physical Gods.
Cloud in Final Fantasy VII is a weird and unpleasant person with a cool-guy-yet-jerk persona, suspiciously spotty memories and a tendency to have head-grabbing freakout episodes at strange times. He's so good at being a leader that everyone trusts him anyway, and push him to carry on even when he flat out tells them that if he does he'll end up going crazy. Even after he's revealed to have been a delusional liar who never really had any of his real credentials, the party is eager to have him back as a leader and overlook it when he starts threatening to dognap Shinra dogs or having claustrophobic panic attacks in submarines.
Merlin of Guenevere frequently zones out at important events (including a state wedding he's one of the officiants for) and says and does seemingly nonsensical things (like handing the Queen of Britain a carrot in the middle of a diplomatic reception), but he's perhaps the most talented and versatile magic users in the game.
In the world of Overwatch several characters dress in costumes simply impractical or just silly for their job, but are allowed to keep them simply by virtue of being so god damn good at what they do. After all, if McCree's one of the fastest guns in the West, does it matter if he dresses like a cowboy? Or if Reinhardt wants to dress in Power Armor with a rocket hammer, pretending to be a crusader and generally Leroy Jenkinsing all over the place, who's going to stop the 8 foot tall, 6 foot wide, musclebound German? And does it really matter if Widowmaker wears shiny purple spandex if she can hit a target at impossible range and see through walls?
In the backstory, Reman Cyrodiil, founder of the Second Tamriellic Empire, was one. Despite his various psychoses and propensities toward violence and decadence, Reman was a very effective leader. Coronated as a child, he proved to be something of a Child Prodigy which, along with his status as The Chosen One (having been born with the long lost Amulet of Kings in hand), he quickly reunited the split halves of Cyrodiil (Colovia and Nibenay) and then the other kingdoms of Men (High Rock and Skyrim). Later, he defeated the Akaviri invaders and absorbed the survivors, who swore fealty to him as a Dragonborn, into his fledgling proto-empire. Though Imperial dogma has mostly covered up or whitewashed his negative traits, he is still (justifiably) remembered as one of the greatest rulers in Cyrodiilic history.
A surprising number of characters in Pokémon fall into this. If you're a highly-skilled Trainer and treat Pokemon with kindness, people are going to look up to you and respect you for it. This means that some rather extreme eccentrics reach respected positions as Gym Leaders, Pokemon Professors, Trial Captains, Elite Four and even Champions.
Sara Valestein in The Legend of Heroes: Trails of Cold Steel is nothing more than the hero's teacher who has no problems drinking off the clock, being messy with her room, and passes work to her students while she just lazes around. She also happens to be one hell of a bracer and is a famous A-ranked bracer called "Purple Lightning".