Another variation has the character introduced as insane ("mad") until they're revealed in the climax, either as a hidden MacGuffin, or a Deus ex Machina. Tad Williams's novel Tailchaser's Song does this to great effect. Less skilled authors may make the "mad" character so annoying that nobody cares during The Reveal.
In the first book of the Mistborn trilogy, Vin encounters a woman named Kliss as an inveterate gossip and something of a ditz. She turns out to be an information seller with a sharp, fairly devious mind.
To a lesser extent, Vin disguises herself as Vanette Renoux, a Rich Idiot with No Day Job, in order to infiltrate noble society, which is mostly populated with more of the same. Even those who catch on that she's not what she appears have no idea that she's a Mistborn.
Later in the series we encounter Allrianne Cett, a flittery pink cream-puff of a blonde noblewoman who not only turns out to be a Rioter whose skill in alomancy is just about the equal to Breeze, but who winds up being an invaluable ally - and who, far from being seduced by Breeze's emotional allomancy, had to use her own considerable powers to seduce him in order to get past the discrepancy in their ages.
Mark Twain wrote about coupling this with Eagleland when vacationing with friends to foreign nations. This was because it was both fun to see tour guides get more and more desperate to impress them, and because... tour guides got more and more desperate to impress the, apparently ignorant, American tourists. Hey, if you got taken behind the velvet rope simply because you seemed unimpressed and ignorant about the significance of some publicly-viewed item, would you be eager to stop doing it?
SiMevolant, of the third Age of Fire novel, spends the whole book acting like a lazy Cloudcuckoolander, until he becomes Tyr by assassinating SiDrakkon and starts acting in a more dominating and focused manner, implying that it was all an act so that no one would view him as a threat.
May Welland of the The Age of Innocence, who acts like a vapid, clueless, superficial socialite. But as the story progresses, it's hinted that she suspects the relationship between her husband and her cousin, and it's confirmed both with the Batman Gambit that she pulls to get rid of the interloper, and 20-something years later, after she's passed away, when her son reveals to his father that she had confided in him.
Granny Lucretia can do it too. In The Liliputian War, she pulls such a trick on Alice and her friends, when they try to get rid of her by saying they're experimenting with very rare and sensitive animals, and she pretends to believe them. And promptly conjures these animals using her illusionist's props.
Marco from Animorphs is a Manipulative Bastard who uses this as a strategy, particularly when he's dealing with adults. In his internal monologue in The Reunion, he comments that adults are more likely to ignore a kid they think is an idiot than one who they suspect is on their level.
Artemis Fowl manages to rob one of the most secure banks in Europe by pretending to be a snotty teenager.
Subverted in that everyone already knows Artemis is a genius, but according to one quote he never lets anyone know exactly how intelligent he is because they would be too scared.
In Below, Dex is a self-taught amateur spellbinder working outside of their guild. He acts like more of a psychotic buffoon than he really is so others won't suspect. Many guilds tend to arrange "accidents" for outsiders, or even insiders who put their skills to ill use.
Some exegesis holds God in The Bible to be using Obfuscating Stupidity most of the time he deals with humans, explaining why he often asks questions to which he already knows the answer. Other exegesis holds this to be simply a feature of ancient Hebrew rhetoric with its rabbinical style of asking rhetorical questions in order to educate one's understudies.
Not entirely stupidity, but more lack of guile as well as lack of physical capability: In L. B. Graham's The Binding of the Blade series, mysterious recurring character Synoki spends four books acting like a crippled, guileless peasant, tramping rather uselessly around with the heroes, before it's revealed in the last book that he's actually a human avatar of Malek, who is essentially the series' analogous equivalent of Lucifer and the Big Bad (andBigger Bad, terrifyingly) whom they've been trying to track down the whole time.
In The Blackcollar, former commando Damon Lathe is a gray-haired, borderline senile war veteran who like to sit around reminiscing about the war, even though he was on the massively losing side. Or so the collaboration government thinks. Right up until he leads a mission to overrun and capture the government center and the spaceport. On twelve hours notice. After waiting twenty nine years.
Played with in Margaret Atwood's short story "Bluebeard's Egg". The protagonist, Sally, spends the whole story fondly mulling over her husband's incredible stupidity, until she finds out two pages from the end that he's having an affair with her best friend and wonders if he's actually scintillatingly intelligent and has spent his whole life playing cruel games with not only her but his previous wives.
In the world of A Brother's Price men are rare and considered emotionally more fragile and less intelligent and driven than women. When kidnapped and tied to a bed, Jerin tries to take advantage of this by whining and using the 'baby words' of bodily functions to make it easier to believe that he's too helpless to try and escape.
Her entire Batman Gambit in the last act is made of this: walk into ambush and let self get caught instead of simply stealthing away... play the bitchy and naive Attention Whore unaware of deeper consequences for one kidnapper... when called on by the criminal leader, upgrades to a Smug Snake attitude and making references that virtually brag "I'm smarter than you" while also giving the impression that she's trying a desperate ploy she just rammed together... that convinces Kali that she is a smart but sloppy amateur in over her head. The fact being that Lucretia is aware that she's in over her head, but is a lot smarter and more calculating than she lets on even when she's talking to Kali about history.
The satirical feminist self-help book Los Caballeros Las Prefieren Brutas (Gentlemen Prefer the Dumb) has this trope as its main thesis: it proposes that the woman should play dumb in front of the man and keep making him pay for everything, even if she has a paying job and can support herself. The reasoning is because many men today both feel intimidated by competent women and dismiss feminine intelligence, a smart woman can use those insecurities and prejudices for her financial advantage by playing bimbo. In the TV adaptation, the main heroine, who is wise about the above point and was given the "too smart" reason as why her (now ex) fiancé cheated on her, deliberately tries to dumb herself down in the hopes of attracting a new boyfriend.
Orr from Catch-22 is portrayed as one of the crazier members of the 256th Squadron, who becomes far more proficient at crashing the airplanes he flies than actually flying them, until it's revealed that he was deliberately crashing at sea as practice so he could fake his death and desert to a neutral country.
The Chrestomanci series has several, but special mention goes to the Duke of Caprona from The Magicians of Caprona. He's only able to retain his position and probably his life by allowing his wife to think he's nothing but a puppet show-obsessed Manchild.
Genji in Cloud of Sparrows acts like a wastrel lord who only cares for women and sake, and goes to view cranes just after the British navy bombards his Edo residence. Turns out he knew (almost) exactly what Kawakami was planning and who was intending to betray him.
Fade appears to be merely Tavi's simpleton slave, who follows him around but doesn't do much. Until he defeats dozens of talented warriors with only his sword, including the man known to be the best swordsman since Araris Valerian died. Turns out, he is Araris, hiding in shame. After that scene, he goes back to being merely Fade, the simpleton slave; only Tavi knows otherwise.
Similarly, Doroga. He appears to be a cheerfully-fugly mountain of muscle, and his favorite weapon is a stone the size of him. However, he managed to teach himself to read in less than six months, is shown effortlessly outmaneuvering Alera's top strategists on the battlefield, and dispenses sage advice to anyone who needs it.
"Doroga does not appear wise..."
In the Company Z novels by J.T. Edson, Sergeant Jubal Branch plays the part of ignorant hick, deliberately mispronouncing words, in order to make criminals underestimate him.
In Robert E. Howard's "The Pool of the Black Ones", Conan the Barbarian realizes that he had accidentally triggered it; his foes probably thought they were herding him into a corner, and that he was stupid. So he takes full advantage of it, nothing being better than being underestimated.
Cameron "Spammy" Scott, from Christopher Brookmyre's Country of the Blind (and others, but most prominently this one) is drug-addled, awkward and more than a little slow. Apparently. But he is also quite intelligent, good with technology, and a very, very good hand-to-hand fighter.
The Culture: In The Player of Games, two of the characters qualify as this, and in both cases, they are doing so to fool both The Empire of Azad and the protagonist, who is basically an Unwitting Pawn being used by Special Circumstances to accomplish the Culture's goals. The Drone accompanying the protagonist initially comes across as bumbling and rather insufferable, but when things get difficult, starts seeming a lot more on the ball in fact, that Drone is the Robotic Psychopath that the protagonist previously knew and is Narrator All Along. There's also Zu, the representative of the Culture in Azad. He comes across as a hedonistic slacker who prefers to party and chase local women. However, he later reveals Hidden Depths and discusses having to have all of his sophisticated Culture implants removed and being under terrible scrutiny. This seems to actually be just a lie to motivate the protagonist to win he's actually a Badass mercenary hired by the Culture.
In Stephen King's The Dark Tower series, Eddie Dean starts off this way because of his crippling self doubt and a lifetime of making himself intentionally stupid/weak in order to protect his big brother's ego. His brother does seem to be at least partially aware of it though, as he once stated that when Eddie is in the zone, he can "convince the Devil to set himself on fire."
In David Copperfield, Betsy insists that the eccentric Mr. Dick is this. Later, she is proved right.
In Maskerade, Nanny Ogg is described as having "a mind like a buzz saw behind a face like an elderly apple". Her "genial old biddy" facade is every bit as formidable as Granny Weatherwax and it's not until you see Nanny Ogg get serious that you realize how she manages to keep up with Granny.
In Thief of Time she showed some of her real genius by keeping up with even Susan Sto Helit.
After Death is fired in Reaper Man, he moves out into the country where his unerring skill at darts earns him the dislike of the other villagers. He quickly uses his exceptional skill to play "badly" for example, bouncing the dart off a post and hitting the hat of the man behind him thus winning everyone over.
Captain Carrot of the Ankh-Morpork City Watch. While usually portrayed as a genuinely uncomplicated character who takes everything at face value, it is observed that "someone has to be very complex indeed to be as simple as Carrot". You can almost see the transition of Captain Carrot from Crouching Moron, Hidden Badass to this trope in Men at Arms. He goes from a person unable to detect irony and having trouble with metaphors to reaching "agreements" with Vetinari and deception. Angua notes in Thud! that
that was Carrot at work. He could sound so innocent, so friendly, so... stupid, in a puppy-dog kind of way, and then he suddenly become this big block of steel and you walked right into it.
In Night Watch he manages to figure out that Commander Vimes has traveled through both time and space, scant seconds after being given a lot of very big words from a Ponder Stibbons, resident Rocket Wizard. This upsets Stibbons because he never expected someone who wasn't a wizard, much less a watchman, to catch on that quickly.
Although Rincewind really is an incompetent coward, some characters are convinced that he's faking it since he has survived multiple situations where, by all rights, he should be dead. If he saw it as something to do as a routine and not a survival tactic, his penchant for running would probably mean he'd get on well with the Archchancellor, who is quite fond of morning jogs.
Though it's unlikely the Archchancellor would appreciate losing a race to him....
He is smart and rational, and his cowardice comes from jaded world-weariness and a sensible fear of the unknown. He's fantastic at improvising his way out of a situation.
Detritus the troll. His basic reasoning may be tied to the ambient temperature (trolls, having silicon-based brains, run hot away from their mountain homes) that puts him squarely in Crouching Moron, Hidden Badass in low temps but he has developed more than a little guile over the course of several books. So much guile that he has been known to remind people of the stereotypes they are supposed to expect from him: No worry I are just der big dumb troll nevermind dis here notepad I am just countin' ma toes. It also helps that he's Too Dumb to Fool to the point that most people don't even try pulling something over on him since a confused Detritus is likely as not to just hit you as a compromise.
Ankh-Morpork's most famous "Legitimate Businessman", Chrysophrase, is also smarter than your average troll, and while he does show off this fact, he has been known to disguise just how much smarter he is, such as intentionally using Hulk Speak when he's fully capable of speaking normally. According to Vimes, he's managed to outthink and outmaneuver all of Ankh-Morpork's native crime lords even when not sitting in a pile of snow.
Camels are the most intelligent creatures on the Disc, or at least the most gifted mathematicians (long desert travel being good for producing such), and smart enough to not show it to humans. How do you think they can spit so accurately?
Lu Tze, aka "The Sweeper", a superlatively multi-talented member of the Monks of History who goes everywhere and sees everything as an apparently brainless old floor sweeper. In places like Ankh-Morpork where people of his ethnicity are uncommon, he and his fellow Monks also ramp up the Funny Foreigner, encouraging further dismissal. He makes a blink-and-you'll-miss-it cameo in several books, in places where something big is about to go down (such as the Temple of Offler in Going Postal). He's also faced down innumerable men with swords, Trolls, Susan Sto Helit, and the Auditors. Remember Rule 1.
For someone who is loud and boisterous, oblivious and thick as a brick, Mustrum Ridcully is a remarkably skilled wizard who somehow manages to make Unseen University run despite keeping wizards under control being akin to herding radioactive cats. It has been noted several times by other characters (and the narrator) that he has managed to be the head wizard of a place where killing your boss in order to get a promotion is socially acceptable for a very long time (almost the entire series). In many cases he seems to let other people think out loud for him while he works out the solution and is frequently Crazy-Prepared. Also his personality radically shifts to a quiet, polite and mature gentleman wizard when he gets to spend personal time with Granny Weatherwax.
He manages to point out in The Last Continent that going back in time to tread on ants is perfectly fine because in a linear universe history 'relies' on you having already done it, which shows that under all that obfuscation there is indeed a powerful intellect.
Otto Chriek, the vampire photographer, plays the Funny Foreigner aspect of stereotypical Uberwaldian vampires to the hilt in order to make humans forget the fact that, if so inclined, he could easily rip them limb from limb.
Lord Vetinari's razor-sharp mind is known and feared throughout Ankh-Morpork, but as soon as someone starts underestimating him he plays into it for everything it's worth. This was his primary weapon in his youth, before he had his reputation and the government behind him, but he isn't above using it even in the present. To the point of pretending not to have solved the case of his own poisoning in Feet of Clay and is later shown to even attend meetings of secret conspiracies against him. In another instance, he uses a particularly forgetful and naïve act in Going Postal while questioning the board of the Grand Trunk Company, and pretends to mix up the term "the glass ceiling" with "the Agateanwall". Mr Slant, a centuries-old zombie lawyer, is onto him though:
Mr Slant was a long-time student of the Patrician, and when his subject appeared to be a confused civil servant asking innocent questions it was time to watch him closely.
Preston, one of the Baron's guards in I Shall Wear Midnight, spends the first half of the book as a Malaproper who does things like confusing "doctrine" with "doctoring", before the mask comes off; it turns out that he actually collects words, reads about metaphysics in his spare time, and became a guard after being kicked out of the priesthood for asking too many questions like, "Is this really true, or what?"
Jingo, has 71-Hour Achmed, the head policeman of Klatch, who acts like a Funny Foreigner in two places. In Ankh-Morpork, he acts absurdly stereotypically Klatchian. In Klatch, he adopts some Ankh-Morpork language and mannerisms he picked up while studying at the Assassins' Guild.
Vimes: I thought you chewed those damned cloves? 71-Hour Ahmed: In Ankh-Morpork, yes. Always be a little bit foreign wherever you are, because everyone knows that foreigners are a little bit stupid.
Granny Weatherwax adopts this trait when playing poker with the riverboat gamblers in Witches Abroad.
It's also Sam Vimes' favorite method of dealing with Vetinari when something is going on that he doesn't want the Patrician to find out about just yet. Vetinari finally snaps about it in Jingo: "If you say 'Sir?' again in that stupid voice, Vimes, I swear there will be trouble."
There's an inversion in The Fifth Elephant, when he tries to show off his diplomatic skills by speaking Ankh-Morpork street dwarvish to a senior Ubervaldian dwarf (imagine addressing the Queen of England in gangsta rap). Mr Skimmer compliments him on his Obfuscating Stupdity as an oblique way of telling him how stupid that was.
Keith in The Amazing Maurice and His Educated Rodents spends the first chapter of the book being called "the stupid-looking kid" by everyone, including the narration, before suddenly making an insightful remark. As everyone stops and stares at him, he patiently explains this trope.
Keith: I'm only stupid-looking. I'm not stupid.
Terry Pratchett has also used this trope outside of Discworld. In Strata, Silver is a Shand, a hulking, tusked bear-like alien, as well as a gifted historian and diplomat. Stranded on a world of primitive humans, she puts them at ease in her presence by acting like the slow-witted pet of her human associate, even performing a "clumsy" dance that conceals her agility and makes them laugh.
Fizban, a wizard in the original trilogy of Dragonlance books often casts spells wrong, is completely senile, and often poses a danger to himself and the heroes whenever they encounter him. Although he does take on a completely different (and scary) personality when angered AND rides a gold dragon, he puts up a particularly hare-brained Dumbledore facade so convincing it has even the reader fooled until near the end when it's revealed that he's actually Paladine, Head god of the good-aligned deities on Krynn in mortal guise.
The same character returns as "Zifnab" in The Death Gate Cycle by the same authors.
The gully dwarves of the setting would appear to engage in at least some of this as well. Sure, they're probably legitimately not the sharpest tools in the shed, but they're still capable of surviving on their own without any help from the other races (that generally look down on them as it is) and deliberately faking some extra incompetence because nobody really expects a gully dwarf to be good at anything, anyway.
In Barbara Hambly's Dragonsbane series, John Aversin adopts what he calls his "dancing bear routine" whenever he has to hobnob with nobility, playing the out-of-touch, ignorant frontier bumbler with no table manners and grins from ear to ear. It's easier to pretend at being an uncivilized, well-meaning slob than it is to try to play by upper-class rules. And besides, people tend to forget that a dancing bear is still dangerous if left unsupervised.
Hendricks is a big muscular man. Made clear in Small Favor, though many fans suspected him as far back as Storm Front. Confirmed in "Even Hand", when he is shown working on his thesis.
Thomas Raith, White Court vampire does this to avoid his older brothers' fate at their father's hands:
"Don't look at me. I'm a drunken, chemical-besotted playboy who does nothing but cavort, sleep, and feed. And even if I had the mind to take a bit of vengeance on the Red Court, I wouldn't have the backbone to actually stand up to anyone." He flashed me a radiant smile. "I'm totally harmless."
Based on a couple of comments made by Lara Raith in Blood Rites, the White Court vamps do this all the time. Since their power structure is all about manipulating events while maintaining plausible deniability, looking competent would merely mean they're not competent enough to appear less competent.
Lara and the Gatekeeper have both remarked on this in regards to Harry himself. The Gatekeeper even told Harry "I can't decide if you are the greatest liar I have ever met, or truly as ignorant as you seem". Furthermore, whenever Lara appears in one of the books, she inevitably gets used by Harry, all while thinking that she's the one using him (at least until the end of the book, when she will realize that Harry beat her at her own game, and then grudgingly congratulate him for it). Somewhat Subverted in that while Harry is capable of being incredibly clever, most of his seemingly idiotic decisions are just that, making him more of a Genius Ditz.
Typical Bad Guy: Spooky. [Dresden] doesn't look all that smart.
Harry's dog, Mouse, is actually far more intelligent than his owner, but plays the dumb Big, Friendly Dog for all it's worth, both to draw attention away from the fact that he is an immensely powerful spirit dog known as a Foo Dog, and because people are uncomfortable around not-overtly-friendly dogs the size of a small sofa. Also, people who like him pet him and give him treats (he may be a super-powerful magical dog, but he is first and foremost a dog).
Ron Carmichael is a fat, balding, middle-aged cop who looks like he sleeps in his suit and has a permanent ketchup stain on his tie. He is also a razor-sharp investigator who prefers to be underestimated.
In Dune, Count Hasimir Fenring definitely counts as one of those. 'Umm-ah-hm-mm-mm', indeed! (He completely loses the affect/speech impediment when in private conversation about the Emperor's orders with the Baron.)
It should be noted that in other books he does this on purpose, both to annoy people around him and to communicate secretly with his wife, who is a Bene Gesserit.
The baron also describes him as "a killer with the manners of a rabbit... the most dangerous kind."
It is revealed in Heretics of Dune that the Tleilaxu have been doing this for thousands and thousands of years simply waiting for the right moment to ascend to power.
Lee is the smartest character in East of Eden, but practices the pidgin Chinese and servant position expected of him. When questioned about this, he answers that the servant position gives him safety and power (he runs the house). Although he was born and raised in San Francisco, and well educated, he speaks pidgin English, because most white people expected it, and wouldn't understand him if he spoke correctly.
In The Elegance of the Hedgehog by Muriel Barbery two of the three main characters, a very precocious 12 year old girl and a middle aged, also brilliant, concierge are both hiding their abilities. The third main character is the catalyst that brings them to each others' attention, and helps them accept their gifts.
Midgety the Ogre from Sukhinov's Emerald City stories. He is fat, appears lazy and dumb buffoon, his clothing is ruffled, his house looks like a mess... and he eats Munchkins that come to his house deceived by the whole outside harmlessness and fall for booby traps he installed everywhere. He is actually very strong, relatively fast for his weight, and he is very cunning, deceitful and ruthless.
Enchanted Forest Chronicles: In Dealing with Dragons, Cimorene uses the fact that almost all princess are feather-headed idiots to try to trick several visiting wizards into thinking she's just as stupid and thus let down their guard around her. Amusingly, she bases most of her ditzy behavior off of things her own sisters did. She suspects that it doesn't really work on them though, and doesn't bother after they figure out that she's smart enough to be a threat to them. The series also suggests that many princesses pretend to be more useless than they're really capable of, because that's the way they're expected to act.
Orson Scott Card's Ender's Shadow series features layers upon layers of geniuses allowing themselves to be underestimated, even by other geniuses who should have known better. The best example would have to be Peter's parents, who were well aware of his and Valentine's political shenanigans in Ender's Game and feigned ignorance so they wouldn't interfere with their children's development. Peter's mother even chews him out about it, being so arrogant in his own brilliance that it never occurred to him he might have inherited it from anybody. To his credit, he's humbled by this when he realizes how obvious it should have been, had he not been so self-absorbed.
This even applies to whole nations, especially when counseled by former military child geniuses. Topping them all might have to be the old USA, which wasn't just a wishy-washy loudmouthed former worldpower in the pocket of China's massive economy, as everybody believed. It was pretty much running the International Fleet all along, and could have made a bid for world domination had it chosen that road. Instead, it used those resources to build and support the first waves of human interstellar colonization, sending humanity (i.e. Americans) out for GALACTIC domination.
In The Exorcist, it's Lt. Kinderman. He calls it "schmaltz". Chris also does her own version of this ("I'm dumb") to get detailed explanations from people. She prefers this method of learning over reading.
G. K. Chesterton's Father Brown has a tendency to stumble around acting dimwitted or like a Cloudcuckoolander (or, in "The Blue Cross", simply acting memorably erratic a tactic to get an inspector to follow him to the criminal) before suddenly whipping out the solution to the case. (Chesterton was making the point that, while many people think of priests as sheltered naifs, that's the one thing an experienced priest can't possibly be he's heard more people confessing to evil thoughts and deeds than any dozen detectives.)
The Finishing School Series: Mademoiselle Geraldine, headmistress of the titular finishing school, appears to be utterly oblivious to its nature as a school for spies, and in fact keeping her Locked Out of the Loop is part of the curriculum. In the final book, it's revealed she's actually a fully trained intelligencer who is every bit as capable as the other teachers.
Flashman is never sure whether his wife Elspeth is really the Dumb Blonde she often seems to be, or is hiding a sharp mind behind her gorgeous face, blonde hair and guileless blue eyes.
In Gene Stratton-Porter's Freckles, when Angel stumbles on the villains who are stealing valuable timber and holding Freckles prisoner, intending to kill him, she acts incapable of understanding and as if fascinated by the chief villain.
In Funeral In Berlin by Len Deighton, the English spy, No Name Given, appears to be not very bright, at least to amateurs. When the assistant to Colonel Stok (a professional Soviet spy) mentions this, Stok tells him that is the height of professionalism.
According to one version of the Bible, Aziraphale (one of the main characters) did this to God slightly after the dawn of time, after Adam and Eve have been cast out of Eden, and Aziraphale gave Eve his sword because he felt sorry for her.
25 And the Lord spake unto the Angel that guarded the eastern gate, saying 'Where is the flaming sword that was given unto thee?' 26 And the Angel said, 'I had it here only a moment ago, I must have put it down some where, forget my own head next.' 27 And the Lord did not ask him again.
Sister Mary Loquacious is initially described as someone who was quite bright, but calls herself a "scatterbrain" because life is easier that way. Later in the book, we see what happens when she has reason to apply her intelligence.
Harry Potter's Dumbledore likes to exaggerate his eccentric old man image to throw others off The Chessmaster scent. Most people are wary of him anyway. There's a reason that an alternate title for Eccentric Mentor is "The Dumbledore". It's more like Obsfuscating Insanity, really. Nobody who isn't deluding himself doubts that Dumbledore is a genius and the greatest wizard of his time, but he tends to come off as a little senile, lulling people into underestimating him.
Technically it's more Obfuscating Inability to Speak English, but the fourth book has Fudge being forced to mime most of what he's saying when he's entertaining the Bulgarian Minister of Magic at the Quiddich World Cup. At the end of the game, the Bulgarian Minister comments in almost perfect English about how well his team played, much to Fudge's fury. The only explanation the Bulgarian Minister gives for the façade is that it "vos very funny".
Not "stupidity" per se, but Alberich teaches the royal bodyguards in Exile's Honor to look just slightly unfocused and unalert, to encourage any potential assassin to discount them.
Mags from the Collegium Chronicles cultivates the public image of being brave, loyal, athletic, good-hearted, and slightly dim. In fact he is brave, loyal, athletic, good-hearted, and the royal spy-master's personal protege.
Agatha Christie's Hercule Poirot frequently represents himself to suspects as a vain, obsessive-compulsive, language-mangling Belgian émigré a more outlandish version of himself, in other words in order to give them a false sense of superiority over him.
"It is true that I can speak the exact, the idiomatic English. But, my friend, to speak the broken English is an enormous asset. It leads people to despise you. They say a foreigner he can't even speak English properly. It is not my policy to terrify people instead, I invite their gentle ridicule. Also I boast! An Englishman he says often, 'A fellow who thinks as much of himself as that cannot be worth much.' That is the English point of view. It is not at all true. And so, you see, I put people off their guard."
Captain Hastings is not this trope, but he discovered a significant clue in The Big Four and Poirot presented him as this trope to British spies. They were impressed with Hastings' act.
At Problem at Mesopotamia, there is a British guy that has an out of focus gaze, relaxed facial muscles, and always looks sad, and it's rumored he drinks heavily. If you are observant, when you go to his office you will notice the door fits perfectly in its frame, and that he adopts an alert posture... fitting for the head of the British secret service.
Will from His Dark Materials, it is mentioned that he is skilled in looking dull, simple and uninteresting in order to avoid drawing attention (he had to learn that in order to protect his mentally ill mother), when he attempts this in front of Iorek Byrnison the latter is not fooled, since the members of his race are Living Lie Detectors.
"One of the major difficulties Trillian experienced in her relationship with Zaphod was learning to distinguish between him pretending to be stupid just to get people off their guard, pretending to be stupid because he couldn't be bothered to think and wanted somebody else to do it for him, pretending to be outrageously stupid to hide the fact that he actually didn't understand what was going on, and really being genuinely stupid."
"He attacked everything in life with a mix of extraordinary genius and naïve incompetence, and it was often difficult to tell which was which."
Admiral Lester "Cowboy" Tourville affected the persona of a brash, loud, and apparently apolitical, well, cowboy, that helped him survive several rounds of State Sec purges in the notoriously unfair Havenite Navy. All that despite being a brilliant tactician and rather ambitious person (the prime targets of said purges) who had a significant role inthe plot that overthrew the Saint-Just regime. He still acts it now, but mostly out of habit.
Obfuscating drunkenness is part of Kevin Usher's defense against the aforementioned State Sec (well, that and being owed a favor by the aforementioned Saint-Just, for his role in the conspiracy to overthrow the Legislaturalists).
"Lesson number—what is it, now?—eight, I think. A reputation for being a drunk can keep you out of as much trouble as being one gets you into." [Usher] padded to his couch and sunk into it. "I've got a high capacity for alcohol, but I don't drink anywhere near as much as people think."
Usher's protégé, Victor Cachat (the student for the aforementioned lessons) learned well. In the short story "The Fanatic", while not pretending to be stupid per se, he convinces everyone he's a brutal, single-minded State Sec officer who doesn't seem to care about any innocents who get hurt while uncovering threats to the regime and punishing incompetence, all the while expertly playing everyone to undermine State Sec control over the sector and ensure the loyalty of the Navy if a revolt against the government takes place.
First, Haymitch started out as a drunken embarrassment on live television, but the minute Peeta and Katniss show they have an ounce of fight in them, it's like flipping a switch. He goes from barely capable of standing to a clever strategist and cunning liar with a cynical knack for thinking outside the box. He wasn't faking the alcholism, however, as evidenced when he goes into withdrawal at one point.
Second, Johanna Mason's entire strategy during her initial Hunger Game was playing a slightly stupid weakling, only for her opponents to find out differently in their last moments.
Ward of Hurog, protagonist of Patricia Briggs' Hurog Duology, started feigning brain damage as a young boy to protect himself from his abusive father. As Ward is officially next in line for his father's title, his apparent incompetence becomes something of an obstacle later on.
Pollio:Do you want to live a long and busy life, with honor at the end of it? Claudius:Yes. Pollio:Then exaggerate your limp, stammer deliberately, sham sickness frequently, let your wits wander, jerk your head and twitch with your hands on all public or semi-public occasions. If you could see as much as I see, you would know that this was your only hope of eventual glory.
This trope drives Robert Ryan's John H. Watson mysteries, in which an aging Sherlock Holmes is a minor character and Watson does most of the detective work. Watson has picked up many of Holmes' observational skills and regularly pulls off a good Sherlock Scan.
In the Judge Dee novel The Chinese Gold Murders, one character is a scribe who is known as Brilliant, but Lazy he is finance savvy, but is also a drunkard and is given to reciting poetry at any opportunity and seems like Plucky Comic Relief. However, circumstances soon appear which presents him as a Diabolical Mastermind in fact, he is on the side of the good guys and is a Master of Disguise he's actually a finance minister who is the twin brother of the novel's murder victim.
Oona in Kiki Strike acts like she can't speak English to get stock and business tips at her nail salon and instructs her workers to do the same.
Lou Ford, the narrator of Jim Thompson's The Killer Inside Me, comes off as a cornball country-bumpkin sheriff with a penchant for faux-philosophical musings ("The child is father to the man") and not an ounce of insincerity in him. He's actually fluent in at least three languages, has virtually memorized his late father's extensive library of scientific and historical literature, does academic-level math problems for fun, and annoys people with the hayseed act mostly as an outlet for his psychopathic sadism (the novel soon provides him with a better one).
No one but Juro in Krabat. (The novel is set in a mill run by an evil wizard. Since he thinks Juro to be dumb and illiterate, he lets him clean up everywhere even in the room with his spellbook.)
He gets it from his mother, the Dowager Duchess of Denver, who uses reams of piffle to hide her intelligence from everyone, including herself. Check out how she figures out that Mary was malingering in Clouds of Witness.
The Machineries of Empire: the drones pretend to be less sentient than they actually are, as they don't want humans to start poking around their private conversations and wondering whether, say, their automated repair tool is plotting their destruction (it's not, but drones value the freedom of movement the assumption of stupidity gives them).
Kruppe, a fat, constantly babbling, Third-Person Person, pastry-devouring thief and mage, is way, way, way smarter than he looks. Underestimating him has had unfortunate results for many characters and he basically runs the city of Darujhistan behind the scenes as the Eel. To be fair, a lot of his closer acquaintances aren't fooled, which he knows and it sometimes seems like he's mainly doing it to annoy people.
Downplayed with Princess Felash. All signs indicate that she is a Royal Brat, and she is, but she plays the extent of it up on purpose in order to seem more harmless and annoying, since no one would expect a capable diplomat and sorceress who can handle a knife as well behind her act.
Miss Marple, also in Agatha Christie's books, passes as a doddering old lady, but has a mind like a razor—or, as one police official put it, "like a bacon slicer".
In Mogworld, Slippery John acts stupid and creepy so that he won't be selected to become a player character.
In the two-volume Mordant's Need series by Stephen R. Donaldson, the hero King Joyce apparently became senile shortly after having done the usual saving the kingdom/world fantasy hero thing, and everyone keeps remarking that if he were his old self, he'd surely be able to come up with a way to deal with the mess they find themselves in today. (Yes, he's faking it; it wouldn't be listed here if he weren't.)
In Loretta Chase's romance novel Mr. Impossible, Loveable Rogue Rupert Carsington loves acting like a "great dumb ox" around the intelligent heroine Daphne, and frequently makes outrageously stupid comments just to enjoy the sight of her in a temper or, in more serious situations, to prevent her from crying or fainting by focusing her energy on rebuking him.
Another bunch of rodents takes this trope even further in Mrs. Frisby and the Rats of NIMH, when the sapient rats convert their Elaborate Underground Base into a replica of a normal rat burrow, destroying all evidence of their civilized lifestyle, to throw their creators from the National Institutes of Mental Health off their trail.
Early on in the original The Mysterious Benedict Society book, Reynie decides when he gets to the Learning Institute for the Very Enlightened to give the impression of knowing as little as possible because the less you know, the less people suspect you, and perhaps the more they tell you.
In The Kennel Murder Case, Liang tries to pull this off with his "can barely speak English" act, and it's implied that he succeeded as far as the Coe household went. Philo Vance saw through the act immediately Liang was educated at Oxford.
Eugenides in The Queen's Thief series plays this differently in every book, fooling the reader for almost the entirety of the first book, and then proceeding to fool people who really, really should know better including, in the third book, the entirety of the country he'd single-handedly defeated in the previous book.
In Redwall, Matthias tricks the sparrows into believing he isn't a threat by pretending to be insane. King Bull Sparra does the same by pretending to be moronic.
The Reynard Cycle: Reynard portrays Rovel (one of his aliases) as somewhat dim in order to seem less suspicious.
In Raymond E. Feist's Riftwar Cycle, there are several characters who fit this trope, namely Nakor, who nearly every single character he encounters makes a comment about him being "more than he appears." He comes off as a doddering old fool at times, a conniving gamblers at others, and one of the four most powerful magicians in the world at others, but is so clearly fighting for the side of good that nobody ever questions him in the least bit. However, it remains a question to be argued over whether he (or Banath) was fighting for good, or just playing around for fun.
Prince Nahrmahn of Emerald in David Weber's Safehold series is known to be far more intelligent than he allows himself to be credited for. Even people who know he's smarter then he seems often underestimate how much smarter.
Simon Templar, The Saint, often uses this technique. He pretends to be a wealthy foppish sucker, and an easy mark for confidence tricksters. He then turns the trick around, and persuades them to give money to him.
The Trope Maker is probably The Scarlet Pimpernel. The Pimpernel's public identity of Sir Percy Blakeney is a total fop (which even his wife believes to be his real self)—a façade to misdirect suspicion that he might be the hero who rescues French aristocrats from the guillotine.
The Seventh Tower has Ebbitt, who is believed by everyone to be insane (and he very well might be), but who also has some of the most extensive and accurate knowledge of the Chosen, their Castle, and light magic in existence. He mentions in passing that he once "chatted" with the Codex of the Chosen (a magical encyclopedia, essentially), which may explain where all his knowledge came from.
In The Heritage of Shannara segment of the Shannara metaseries, it is revealed that Cogline, the crazy old man first introduced in the original trilogy, is actually an extremely long-lived ex-Druid and a master of the old sciences who was only faking insanity for the sake of his own survival. Apparently he almost actually did go mad, but somehow stayed sane, and later became Walker Boh's mentor a close friend.
Song at Dawn: Alienor's ladies-in-waiting appear to be Upper Class Twits gossiping about fashion and other frivolity but they are actually cunning information brokers mining valuable intel from seemingly meaningless chatter. The trick is telling the faker from the genuine twit.
Daenerys figures out pretty quick that people will underestimate her because of her youth and gender, so she starts playing it up, saying things like, "I am only a young girl and know little of such things, but..." to the point that it becomes a catchphrase. Specifically, it becomes a catch-phrase that her advisers in the kingdoms she's conquered interpret as implicitly sarcastic and a signal that they should probably shut up before her patience with their stupid or unacceptable suggestions runs out and she has them demoted or outright executed. She is, after all, only 'the nice one' in comparison to her brother, and she has massive carnivorous monsters to feed, who have already fried some rather important people at her apparent whim.
Go ahead: assume Olenna Redwyne-Tyrell is merely a sharp-tongued harridan who occasionally misplaces her words (and even names) in the possible onset of dementia and is just counting down the days until she pegs it, content to merely short-change merchants and middlemen who try to diddle her and whose major hobby is berating everybody in earshot as to their shortcomings as she leaves everything major to her sons and grandchildren. On your head be it.
Lampshaded by Dontos The Fool to The IngenuePrincess Classic Sansa Stark. She laments her own naivete in the game of thrones, but Dontos points out that all The Chessmaster characters watch each other like hawks, but pay little attention to those they think are stupid. Sure enough no-one suspects Sansa is planning an escape with Dontos until after it happens.
Jim Butcher is VERY fond of this one: In his Spider-Man novel The Darkest Hours, Rhino, who has a normal level of intelligence, pretends to be dumber than he is so the rest of Spidey's villains, many of whom are of genius-level intelligence, will underestimate him.
The Klingon Grodak in Star Trek: Seven Deadly Sins. It leads to protagonist Toqel (a Romulan politician) severely underestimating him and the Klingons in general, with troubling results for the Romulans and fatal ones for Toqel. Grodak was relying on Toqel's Romulan pride and arrogance to blind her to his games.
The Klingons tend to pull this trope quite often in the Star Trek Novel Verse, their enthusiastic bluster, casual violence and fondness for drink disguising the fact that they're every bit as capable of cunning manipulation as any other race; indeed, they're actually extremely political, for all their talk of "warrior's honour". Another Klingon character who illustrates the trope perfectly is General Khegh from Star Trek: Titan.
An early book, The Courtship of Princess Leia, introduced and killed villain of the book Warlord Zsinj, a hammishly over-the-top fat egocentric idiot who somehow happened to command a large fleet. Books in the X-Wing Series, written later but set before, Retcon him into being much more competent and deliberately putting on a faintly absurd act, knowing that most of the people he was around could see through it and would be a bit confused. It's effective enough that he was the first character considered dangerous enough for The Alliance and The Empire to work together against.
Meanwhile, in the Hand of Thrawn duology, Moff Disra had a very bland military aide, Major Grodin Tierce. Disra, looking up his aide's records, found that he was actually a Royal Guard that is, the best of the best, a really good fighter confronted Tierce about it, and... well. As part of a Big Bad Duumvirate, Tierce dropped the clueless act, letting people see him as a dangerous fighter, but whenever Pellaeon was around he took it up again. Tierce is a human clone with a little of Thrawn's mind in him.
Suddenly the diffident and marginally competent Major Tierce who'd served as his military aide for eight months was gone. In his place stood a warrior. Disra had once heard it said that a discerning person could always recognize an Imperial stormtrooper or Royal Guard, whether he stood before you in full armor or lay dying on a sickbed. He'd always discounted such things as childish myths. He wouldn't make that mistake again.
For that matter, the third member of the triumvirate had it pretty much in reverse. He could pull off a Thrawn impersonation to the point of having Thrawn's powerful, regal air, but his tactical knowledge was that of a con artist. When only the other members of the triumvirate are around he drops it.
Survivor's Quest has the slavetaking nomadic Vagaari passing themselves off as Geroons, one of the people they took as slaves. As Geroons they fawn all over the Chiss and the Jedi and act like harmless cowards. But the Chiss know what they really are, and with the Jedi's help Out-Gambitted them handily by the end of the book.
In the beginning of Legacy of the Force, you'd think that Wedge Antilles couldn't pull this trope off. But he does he's been retired twice now and is in his sixties spending all his time with his family and writing his memoirs, so he couldn't be too much trouble, right? It doesn't take long before the act, if it was an act, is dropped.
In the William Shakespeare's Star Wars series, Ian Doescher rewrites Jar-Jar's character so that instead of actually being stupid, he only plays the fool as part of his Batman Gambit to unite the Naboo and the Gungans. (When he's by himself, his soliloquies are quite eloquent.)
Emperor Sarabian had the entire court in Matherion convinced he was either an utter dolt, a harmless fop, or a simple fool easily distracted by his silly hobbies. He reveals the truth to Ehlana, Sparhawk, and the others, and eventually proceeds to overthrow his own government, take proper control of the empire, single-handedly remove all the corrupt courtiers involved in a failed coup, and become a wise and effective ruler. And he has such a delightful time doing it.
His act was one of necessity as the Vast Bureaucracy, having taken power generations ago, assassinates any Emperor intelligent enough to take it back.
Elysoun, one of Sarabian's wives, is viewed as an empty-headed Lovable Sex Maniac due to her culture's practice of free love and her traditional costume leaving her breasts bare. While she does enjoy her liaisons, Elysoun is also very intelligent and loyal to her husband. When one of the wives plots against their husband, Elysoun uses her reputation to uncover the details and thwart the attempt.
Melidere, one of Queen Ehlana's ladies-in-waiting, is smarter than most people, but masks it under the appearance of a Dumb Blonde.
Sun Kai, in the Temeraire series, uses a form of Obfuscating Stupidity to trick the main characters into ignoring him when he's in their presence. It later turns out that he is, in fact, an ally.
Jupiter Jones from The Three Investigators is the smartest person in the group, but because he is a former child actor and a little plump, he can act unintelligent in order to disarm people and get information from them that he wouldn't get otherwise.
Dolphus Raymond in To Kill a Mockingbird channels this, carrying around a bottle of what everyone thinks is whiskey in a brown paper bag (it's actually Coca Cola) and drinking from it. People use alcoholism to justify his "strange" behavior (being a white man married to a black woman in Alabama in the early 20th century).
Sir Myles of Olau is a mild case. People respect him and know he is wise, but that doesn't stop him from being the court's drunk. Which allows him to see and hear a lot more than most people. By Protector of the Small, he's dropped the act somewhat. Being the king's official spymaster will do that for you.
Thom was probably the best example. He fooled all his teachers for years until he stopped pretending to be dumb and passed the highest exam to become a sorcerer.
The wizard Farmer Cape from the Beka Cooper trilogy does this as well. In fact he seems to have two layers of deception. He acts the part of the country bumpkin around those he knows are enemies, then, when he's around people he thinks he might be able to trust, he drops it for a goofball persona that is a good deal smarter, but still obscures his true genius and Crazy-Prepared nature.
Another great example is Aly from the Trickster's Duet. Most people who run into her think she's just an average, somewhat dim and racist house maid when really, she's the spy-master helping orchestrate a rebellion. (That said, the more intelligent characters manage to work out the truth fairly quickly.)
Vorkosigan Saga: Despite his nickname, if Ivan "You Idiot" Vorpatril from Bujold's various Miles Vorkosigan books is any less bright than his aforementioned cousin it is by a percentage point or two topsnote (far too many "stupid questions" has set said cousin on the right track to dismiss as coincidence). He is also somewhat lazy, distinctly unambitious, and widely regarded as being a few heartbeats from the throne of Barrayar; the latter of which makes him rather loathe to seem more than an idle cad of marginal competence. He habitually avoids any heroics he can unless he is blatantly a lackey bullied into assisting more overbearing/proactive sorts, and as for politics...
...it was not that he ran screaming when the loaded subjects arose; that would attract too much attention. Saunter off slowly, that's the ticket.
The White Queen in The Unexplored Summon://Blood-Sign claims that she never bothers planning anything, since (being the strongest being in the setting) she doesn't need to. She also gives the impression of a Woman Child who's hopelessly obsessed with the main character Kyousuke. However, this is (mostly) a facade, with later books confirming that she's far smarter and in control of herself than she claims. Notably, in the seventh book, she concocts an elaborate plan in which she disguises herself to get close to Kyousuke, while giving enough hints for him to realize the deception. This tricks him into thinking the disguise is her real plan, allowing her actual one to succeed.
Planetary governor Grice in the Warhammer 40,000 novel For the Emperor seems to be petty and stupid, as well as possibly corrupt, his foolish actions exasperating a potential conflict with the alien tau. He's actually a tyranid mutant purposefully trying to create conflict among the locals to make it easier for the tyranids to invade.
When Justice J.J. Ford and Florence Baumbach have lunch together, it's mentioned that Ford deliberately would pretend not to know about the tuxedo and dress shops Mrs. Baumbach was talking about, "to keep the witness talking". She really didn't know, but would have pretended not to anyway.
The real surprise is that Sandy McSouthers, the not-too-bright former boxer, is Sam Westing himself, and he manages to fool everyone, even the people who had met him in person as Sam Westing, until almost the very end.
Verin Mathwin from The Wheel of Time certainly qualifies as using this. Using her membership as a Brown Ajah, she hides her identity as a brilliant, centuries old mage. Not only is she a member of the Black Ajah (a secret society of Aes Sedai devoted to the Dark One) who only joined their ranks to ferret them out and betray them, but she is so good at hiding this very fact that she can do it in chapters of the books that are written from her own point of view. Her final admission of her membership, handing over of everything she'd found out, and subsequent death qualifies as a Moment of Awesome in its own right.
Mat plays this tropes straight for the first three books or so, then tries to invoke it every chance he get.
Wings of Fire: In Moon Rising, Qibli acts dumber than he is to fit in with the other students. If not for her telepathy, Moon would never have realized how clever he really was.
Leopold plays up his image as a dandy, spoiled princeling to hide his participation in the Long Game.
Eren has been feigning alcoholism for the past dozen or so years so that people would underestimate him.
In Wolf Hall, Jane Seymour presents herself as a naive Shrinking Violet while serving as one of Anne Boleyn. She also isn't as educated as most of them, knowing only English and having been taught more hunting than reading by her father. When at home or talking to Cromwell, however, Jane shows more wit and insight, and while her sister describes her as a woman who's always waiting for a man to tell her what to do, that doesn't necessarily mean she'll listen. While she does seem to be genuinely kind, she's quicker than she lets on, as becomes evident in the way she handles Henry's attention.
The Zombie Knight has Parson Miles and Overra. Their joint career is riddled with boneheaded mistakes and failed missions, yet if you consider the full consequences of those mistakes and failures, they almost invariably result in a net gain for the Vanguard.