This episode of SMBC Theater gives us a plumber with rock bottom prices, high skill and reliability, amazing punctuality ....and an insistence that customers watch him act like a plumber in a porno movie. Yes, both the male and female customers. When questioned, he will immediately say he is the best value in the city.
Matthew from Critical Hit plays Torq, his Half Orc Fighter, like this. Out of combat, he is stupid, tends to blurt out inappropriate things and is described as having a constant vacant expression. However, he gets a + 11 to his attacks, and in combat becomes a whirling dervish with a giant axe.
Bugs, a brilliant deviser and gadgeteer in the Whateley Universe. Her intense fascinations with rabbits, sparkles, and building things in egg shapes is completely accepted (usually) because she's just that darn good as an inventor. Oh, and she's the most gorgeous inventor at Superhero School Whateley Academy so she gets lots of slack.
Jade, and actually most of the Kimbas who are the main cast, might fall into this category. Jade self-mutilates, talks to herselves (okay, yes, she can psychokinetically charge things with a copy of her persona, but they have interactive conversations, and argue with each other, and they in of themselves have quirks, like the Spy Specks all wanting to be Jane Bond with a middle names to differentiate.), chooses to wear both wear armbands that define her as an ultraviolent and a pacifist, has an unhealthy fixation with Hello Kitty. Yes, despite all this, she is brilliant in so many areas, tactically, technically, improvising, and general mayhem causing.
Ayla is so good at business and math, that as a freshman she has been assigned to be the teacher's aid in every level of the classes relating to those, she plans and back up plans and back ups to her backup plans (we're talking that during a team tactics class, when put in situations where one of the team has turned evil, she doesn't just have one or two plans, but i n the case of a couple of her teammates, she has plans that go past plan Z and start getting into double letters... this is over 27 plans to take down members of her own team, not other training team's members, but to take down her friends), however, she is extremely elitist, scoffs at most food as inferior and has finagled the school chefs to make her surprise special top cuisine meals, is extremely serious (not just for a teenager, but for an adult), even having a quote unquote 'The Queen is not amused' look, which is saying alot since one of her teammates is actually the host to the essence of an ancient Sidhe Queen, and even the Sidhe Queen thinks Ayla is to serious and haughty.
Chaka is... I think someone else should explain all the awesomeness and insanity of the Soke no Do, a martial artist that can do any martial art trick and them some, but likes to use chi to wedgie people, created a chi attack which she fires from her finger like she is shooting a gun while yelling "CHAKA CHAKA BANG BANG" based off the Kamahameha from Dragonball/Dragonball Z, and when she was given a pair of power gloves which would quadruple the strength of her punches twice a day but required a command phrase, so she chose "IT'S CLOBBERING TIME!!!" and got Ayla (who bought Marvel Comics in canon) to approve her using it so she doesn't violate trademark infringement laws.
kitten (the lower case k is deliberate), a transsexual goth who functions best when being led around on a leash by her boyfriend, spells her name with a lower case k and is a powerful teleporter psychic and the mainstay of the human invasion of Hell in The Salvation War.
Brigadier General David Adams of Survival of the Fittest spin off The Program. His antics include spontaneously breaking into the American national anthem during an announcement (when he's supposed to be reeling off who died), making bizarre jokes, contradicting himself midsentence and thinking out loud (both also in announcements). For all that, The Program was his idea, and given the setting, there's no possible way he can be an incompetent leader or tactician.
This Onion article is about a Bunny Ears SWAT team operative.
Most people in the Global Guardians PBEM Universe see the homeless, clearly schizophrenic "superhero" known as Mister Easter as this. (He's a deluded religious fanatic thinks he's been given a mission from God to fight evil, despite most of his powers being utterly useless in fighting crime... things like being able to turn water into wine, curing leprosy at a touch, and coming back from the dead after three days). But then New York City was invaded by an army of vampires, and suddenly Mister Easter turned into the hundred-megaton nuclear weapon of anti-vampire superheroes.
Spoiler Warning has Reginald Cuftbert, who embodies Leeroy Jenkins, uses weapons he has no training in and wears a bonnet into battle. He also happens to be extremely efficient at killing anything he's asked to.
RWBY: Professor Peter Port's idea of teaching a lesson involves regaling the students with a story of the time he captured a live Grimm, making bad jokes, and hitting on the pretty female students (to Yang's disgust). But he is an excellent teacher and mentor. How excellent? After one conversation with him, Weiss stops treating Ruby like crap, stops demanding to be made the team leader, to making Ruby coffee so she can keep studying. She's been the perfect team-mate ever since.
Red vs. Blue: Honestly, all of the Blood Gulchers fit into this trope in one way or another. Keep in mind that they were selected from the worst of the worst soldiers so that Project Freelancer could test their Super Soldiers.
Sarge is a General Ripper and The Neidermeyer who constantly comes up with dumb and bizarre ideas to beat the Blues. He's also skilled enough to make robots and turn people into cyborgs, deadly in a fight, and managed to outsmart and defeat Agent Washington.
Grif is generally known for his uncleanliness, laziness and cowardice. But when he's called to action, he leaps into action without a second thought. (When fighting against the Meta in the Season 8 finale, the Meta's been beating the Reds and Tucker to hell and back with his weapon. Grif uses his weight to his advantage, and leaps atop the Meta, stealing his weapon and giving his allies a chance.)
Donut may come across as Ambiguously Gay, but his grenade tossing abilities are not to be underestimated. Seriously, he threw a sticky grenade halfway across Blood Gulch into Tex's lap, and she was operating the Blue's tank.
Caboose is the resident ditz of the group, with a very loose grasp on reality, but if you know how to order him about, he's a force to be reckoned with. And don't even get started when he goes into Unstoppable Rage mode...
Wal Bunkley, Mayor of Funkytown in thisLet's Play of SimCity 3000 is barely congenial to most of his constituents, has a "Maybe Later" sign made to brush off petitions he doesn't want to deal with, and is probably the only politician to tell the people of his city that they're "fucking awesome" (in the immediate aftermath of a devastating earthquake). He manages to stay in office for a hundred years and runs a very effective ship.
In The Thrilling Adventure Hour, Frank & Sadie Doyle's constant drunkenness and general apathy to anything that is not either booze or each other masks a truly masterful knowledge of the occult and an ability to confront supernatural baddies at every turn.
Noob: La Quête Légendaire introduces Abraham Lepape, a mafia big wig pretending to be a priest who can't remember which of his three sons an ex-girlfriend of his gave birth to.
The Ultramarines are an entire army of Parody Sues who speak in Purple Prose and can't shut up about their grandoise, but when something has to be done, they will do it, even if it violates all the rules of physics and common sense.