Dax from Greystone Valley is introduced as a crazy old man who does nothing but complain and possibly eats bugs. Then it comes time to break out of a dungeon, and it turns out he can hold off a veritable army on monsters single-handedly.
Zhong Botong, the Old Urchin from Legend of the Condor Heroes. He's a very old man who behaves like a little kid, throwing tantrums at the most absurd things and enjoying causing confusion. When it comes to kung fu, however, run for your life: by the end, he's among the top five martial artists in the world.
Redwall: King Bull Sparra does this really well. Maybe a little too well...
The character of Alfred from The Death Gate Cycle, written by Weis & Hickman, is an over the top example of this trope. He first appears as a stumbling, clumsy butler, but in dire circumstances, at times off-screen, he is the pinnacle of his wizarding tradition and can perform miracles in Functional Magic up to and including resurrecting the dead, the right way, whereas other mages can do so only by draining the life of another being of the same race, somewhere in the multiverse. Of course, a lot of people want to get hold of Alfred for his magical prowess. Problem is, he doesn't remember how he pulls his magic off, pulling a complete black-out, more than often enough accompanied by an undignified fainting. It eventually turns out that he originally just used Obfuscating Stupidity to avoid revealing his powers to the world — but over time, it became so in-grown that he practically forgot how to use his powers at all.
In the same series, a character named Zifnab appears to be a senile old man who can't remember the color of his own robe. He is later discovered to be one of the oldest living beings in the universe. Although he is afflicted with Alzheimer's, he is questionably the most powerful magician in the series, complete with his own pet dragon.
I always thought it was less Alzheimer's and more way too many bad memories from when the world as we knew it was broken asunder and billions died. You go around with that mucking up your head and you would be daffy yourself.
Then of course there's the absent-minded, bumbling elderly mage Fizban, from Weis & Hickman's Dragonlance series. Though occasionally his spells prove useful, this is mostly by accident. Later you learn the truth: he's actually the God the protagonists are fighting to bring back...
Title character Harry of The Dresden Files, to those who do not know who he is and what he is capable of. He tends to utilise this and a constant stream of sarcasm to pull Obfuscating Stupidity on his opponents, many of whom are in strict terms far out of his weight class.
People consistently underestimate him, or are utterly terrified of him. You kidnap his girlfriend, he'll destroy you and your servants horribly, starting a war in the process. Take his daughter, and he will commit genocide.
In his first appearance, Mort the ectomancer had been seriously letting his talents atrophy, and even when he gets his act together later, he's quite adamantly not a fighter. Because of this, while Harry says repeatedly that Mort has a huge amount of power in his field, we don't really see him doing a lot with it. And then along comes Ghost Story, and... we do. Perhaps most notably, toward the end Corpsetaker kidnaps him and trusses him up over a pit full of minions, only to realize a little too late that leaving someone with the power to control ghosts dangling above a small army of crazed, murderous spirits was a terminally bad idea.
Lords and Ladies - When Lancre is under siege by elves, perpetual milquetoast Magrat gets her Hidden Badass moment after she dons the war armor of Queen Ynci the Short-Tempered. She then proceeds to kick elvish ass (including shooting a crossbow through a keyhole) and ride off for a showdown with the Queen of the Elves. Near the end of the novel, we learn that Queen Ynci was a fictional creation of a former Lancre monarch.
Magrat isn't a "moron," but she is usually timid and woefully na´ve.
Also in the volume before that, Witches Abroad, where two scary snake-women look upon shy Magrat as some kind of small furry animal, but when they corner her they find out to their cost that the small furry animal she resembles is a mongoose.
Men at Arms - Detritus, a particularly dumb troll, becomes temporarily hyper-intelligent when he's locked in a cold room and his silicon brain starts super-conducting.
A.E. Pessimal from Thud! has his badassness hidden so deep that even Vetinari himself is completely surprised and confused when he hears Pessimal attacked a troll. With his teeth.
A constant example given are the wizards; Seen one way, they are rather large, simple minded men who like big dinners and tend to argue with each other, with a tendency to regard the end of the world as a minor curiosity. In another light, they are an elite group of men who are given quite a bit of leeway in return for consistently and conscientiously refraining from causing the laws of causality and physics to metaphorically do handstands and jump through hoops. It's not difficult at all to refrain from turning people into small amphibians when you can't, but it's much much harder when you know exactly how easy it is. On top of that, the natural number of wizards is one, and the arguments they have are harmless ways of expressing that, rather than, as it was in the past, all out thaumonuclear war. There are places on the Disc where the wizards weren't quite so harmless and simple minded; grass may never grow there again and you're lucky to leave one the same shape as you went in.
Sourcery states that historically the plural of "wizard" has been "war". And while UU has sufficed to largely sublimate the natural tendency of wizards to leave large smoking craters in the landscape in favor of petty arguments about who took the last macaroon, occasionally the faculty will decide to work more or less together, and when they do they are indeed a potent force.
Lennie from Of Mice and Men may be a mentally impaired Gentle Giant, but that doesn't mean you can just push him around. Curley finds out the hard way.
Eddie Dean in The Dark Tower is a washed-up cynical junkie loser when he first falls into Midworld, and seemingly dependent upon the Last Gunslinger for basic survival. He reveals himself to be a talented gunfighter when provoked.
The wizard Schmendrick of The Last Unicorn is, at times, capable of awe-inspiring magic...the trouble is, he can hardly ever get it to work, and usually it doesn't do what he expected. But he gets it under control in the end.
In George MacDonald Fraser's McAuslan stories, Private McGlinchy is, in a football game, either completely useless or completely amazing, depending on factors that other characters are trying to figure out.
Fraser pulls it again in the Flashman series, with Flashman's wife Elspeth. Flashman regards her as a dunce, and she certainly seems shallow and vapid, but in Flashman's Lady and even more in the The Subtleties of Baccarat, she proves to be a vicious little minx that you trifle with at your peril. The crowning irony is that Flashman never figures this out, even though he's usually so perspicacious about others' strengths and weaknesses, and he's married to her for sixty years.
In Raymond E. Feist's Riftwar Cycle, a gibbering, mindless beggar barely capable of feeding himself is later revealed to be the mortal shell of Macros the Black, the most powerful sorcerer in the world. His mind was not in his body, until suddenly it was imperative for him to be present to fight the darkness and chaos.
And then there's Nakor, a wandering con man and chronic goof-off who just happens to know more about magic, the nature of the multiverse, and beating down evil than anyone else in the series, with the possible exception of Pug.
Alan Dean Foster's Spellsinger series has JonTom Merryweather, the spellsinger of the title. A modern human in an alternate, medieval-equivalent universe filled with Talking Animals, who is pretty much useless in a fight, at least in the first few books...except for his spellsinging, which is the ultimate wild card and capable of doing anything he can sing about. The only trouble is that 1.) he has to know the right song, 2.) sometimes nothing happens, and 3.) even he's not sure what's going to happen when he starts. It's done everything from switching the entire party's genders, to changing a wizard's apprentice into a phoenix, to summoning a god.
Some stories of Ganesha present the jolly Big Eater god as equal in power to his fearsome father Shiva, capable of stopping the sun and destroying the world, but luckily too nice to do so.
The novel Armor by John Steakley follows two storylines set about five years apart, with the earlier one framed by the discovery of the Powered Armor used by the earlier protagonist on a distant, non-wartorn colony in a crashed escape pod. The armor's owner, Felix, is quite literally an unstoppable killing machine: in a war where no one has survived more than ten major missions, armor notwithstanding, Felix makes it through over twenty before being killed by another human soldier. Meanwhile, in the present-day, a rebellion is brewing right underneath the nose of the colony's drunken, dimwitted owner, Lewis, causing great consternation to the present-day protagonist...especially when it breaks into open war and a nearby space pirate decides to capitalize on the situation. With a military grade dreadnought. Fortunately, Lewis is Felix, lying low and enjoying life. At least, until he decides to save his colony by putting his armor back on, slaughtering an army's worth of pirates, and then takes down the dreadnought with his bare damn hands.
Neville Longbottom of Harry Potter, although he worked hard to achieve the Badass designation from the Moron.
Culminates in a Crowning Moment of Awesome. Consider also that the prophesy nominating Harry as "the chosen one" easily applied to Neville as well. The fan meme is, "Neville is the Boy-That-Could-Have-Been-But-Did-Anyway."
Let's face it; this trope could easily be renamed "The Neville."
Luna Lovegood as well.
Even Ron a few times.
And Umbridge, in the reverse.
In the books Operation: Red Jericho and Operation: Typhoon Shore, Posh Charlie has a very minor role and is known for his constant stuttering and nervousness. Put him in a combat situation and he becomes a confident soldier, immediately dropping the stutter. This may possibly be Obfuscating Stupidity due to the knowledge in the latter book that he is actually a very competent researcher.
Lovable the raven, from the Firekeeper series, is described as a "bubble head" and has a love for anything shiny. This is in stark contrast to her far more serious mate, Bitter. However, in the fifth book, Wolf Hunting, when Bitter and Lovable are ensnared by magic vines that can kill their victims, Lovable forgoes her shot at escape to stay and keep the vines from getting Bitter completely. She manages this for quite some time until help arrives and is the only reason that help wasn't too late for Bitter.
Ceallio, in Tad Williams' Memory, Sorrow, and Thorn series, is a mute simpleton when he is discovered by the protagonists working in an inn in the marsh town of Kwanitupul. However, it turns out that he's really the famous knight Camaris, who suffered a Heroic BSOD and attempted suicide many years ago. When sorely provoked, he displays incredible strength and fighting skill, first beating up a group of thugs and then defeating a Nabbanai nobleman in a swordfight, but remains in a childlike daze. It is not until he's brought to Prince Josua that he finally recovers his wits.
Orbek Black Knife from Blade of Tyshalle. The above quote comes right after Orbek's Crowning Moment of Awesome. The irony lies in that Caine originally targeted Orbek first when breaking up Orbek's old gang because he thought the young ogrillo was the gang's weakest point.
The Belgariad and Malloreon have several of these and several subversions. Played straight with Silk who normally plays the thief/rogue member of the cast, but in The Malloreon when Bethra is murdered, he tortures the killer into revealing who hired him and then proceeds to assassinate half the family before being stopped by his companions. Later, when the Dagashi assassin Brill pisses him off at Rak Cthol, he beats the hell out of him and kicks him off the mountain. He then coolly informs Belgarath that Brill was learning how to fly, and not all that successfully. These were, of course, Crowning Moments of Awesome. Also in the same series, when Belgarath gets pissed he has been known to destroy entire mountains and also buries Zedar, who betrayed him and his master, alive for And I Must Scream - the horror here coming from the fact that Zedar is effectively immortal and no wizard can undo what another wizard has done, so Zedar will be entombed in solid stone for all eternity. He likes to let the world think he is a Dirty Old Man, and he likes to make remarks of his time with the fully female Dryad race and of the very open-minded Marag women. He also tends to become badass when his family is threatened.
Brill himself also counts. For the first two books he appears to be a footpad and hired thugh for Asharak, the starter villain. He's easily evaded by the cast, and the only remarkable thing about him seems to be his ability to catch up with them. And then in book three he reveals that he's a freaking ninja. And that Asharak was probably working for him and not the other way around. This culminates in his battle with Silk, which is pretty epic for both combatants.
Tyrion's squire Podrick Payne in A Song of Ice and Fire. He's tongue-tied and incompetent most of the time to the extent that Tyrion suspects the boy was inflicted on him as a joke, but when Tyrion is caught on a bridge of wrecked ships on a burning river with Ser Mandon Moore, one of the elite Kingsguard, trying to kill him, Pod somehow manages to kill Mandon and drag the unconscious Tyrion to safety. He's also seen cutting down a few enemies when Tyrion storms out to meet Stannis's men.
This is a characteristic of Hobbits as a whole. As a race, they spend most of their time eating, drinking and making sure they have enough to eat and drink (the only function of their police force — the Shirriffs — is to chase off wild animals). Yet as Wolves, Orcs and Saruman have found out, there's only so far you can push them.
From L.J. Smith's Night World series, Iliana Dominick spends most of the story as The Load and The Ditz, but when her friends and bodyguards are threatened at the end of the book, she finally unleashes the magic in her blood that she's been denying her entire life.
The Codex Alera series gives us the slave Fade. He's not just a moron, he's obviously severely brain-damaged, and is generally not much good for anything but some minor blacksmithing. Except that he's actually a legendary swordsman believed dead by the rest of the country, and he will miss you up bad if given a reason to do so. He's also much, much smarter than he acts, and the only reason he's acting as a slave is to keep an eye on Tavi.
Fishlegs from the How to Train Your Dragon series. He's described as looking like a 'stick-insect with asthma, eczema, and the face of a fish', and doesn't really like adventuring. However.....Fishlegs happens to be a Berserk, one of the wildest and most respected types of Viking.
The Culture is normally regarded as being hedonistic and extremely eccentric by most members of the galactic community. This doesn't just include the biological citizens, but the godlike AI's with 6 figure IQ's, and almost every single one of their starships are like this too. Most non-Culture sentients consider it strange that the Minds can be bothered to care about beings so intellectually below them. Similarly, a lot of starships give themselves silly / ironic names, and are often fully developed personalities. Despite this apparently goofy, peaceful image, if you threaten the lives of the Culture's citizens, pray that they only declare war on you. You WILL lose, but are most likely to be killed in a swift and conventional way. If not, then you can look forward to being killed in the most obscenely painful manner possible.
"Do Not Fuck With The Culture".
And you know you're completely fucked when you've attracted the attention of Special Circumstances. Completely fucked. You'll be lucky if they don't just destroy your entire civilization from the inside out and re-make it.
That includes any of their happy-go-lucky agents.
Just to add, do not ever try to pull one over on a Mind. Especially the Eccentrics (Grey Area, anyone?)
Telnan, introduced in the Dragaera novel Dzur may carry a terrifying soul-destroying Empathic Weapon, but he's a cheerful, ditzy guy, and not too bright. However, he still very much fits the Proud Warrior Race Guy and Blood Knight credentials of the Dzur, and he's somewhat more competent than he initially seems.
In the Sword of Truth novels, Zedd is initially known to the reader as a goofy old man who's introduced talking to clouds. Naked. What the reader finds out later is that he was once known as the "Wind of Death," is a wizard of the first order, and in the past earned that nickname by winning a magical war.
Other wizards in the series fit the mold in one way or another, such as Warren who's a total nerd and Non-Action Guy until he and Zedd go to show an opposing army "an old fashioned firefight", and Nathan, who is described at one point as a "1,000-year-old child", but is as clever and deadly as they come.
Somewhat of a subverted trope, but Orion in Artemis Fowl and the Atlantis Complex. During the penultimate scene, Artemis realizes that his brains are useless and uses electricity to switch back to Orion. As Holly states, "Artemis can't shoot." But Orion can.
When we meet Matrim Cauthon, he plays pranks, jokes around and generally serves as the comic relief in the group of main characters. He then gets cut by an evil knife and gets infected by said evil. Barely out of his sickbed after a major healing, he stumbles out on a training field where arguably the finest swordsmen in the world are training, and needing money, challenges two of them at the same time to a fight. With a quarterstaff, he wins. The he takes a level in badass.
Those who grew up reading the books of Lloyd Alexander will remember the bard and minor king Fflewddur Fflam, who at first seems like only a half-trained musician with a gift for exaggeration and a magic harp that calls him on it every time. But drop him in a fight with something important at stake and you realize he's also a capable and dangerous warrior...though still one with his heart in his mouth until the battle is over.
Stephen King and Peter Straub's collaborative book The Talisman has Wolf— a lovable, simple-minded Gentle Giant who serves as a shepherd in an alternate Earth and tags along with Jack in his quest to save his mother. He's also that dimension's version of a werewolf. And has adopted Jack as his new "herd". And is impossibly strong even when he isn't transformed. Which means that you really, really want to think twice about hurting Jack.
Jack the Ripper in Time Scout forms a rare duo. He's two people, one a patsy being hypnotically controlled and turned into a weapon by the mastermind.
The Clutch Turtles from Sharon Lee & Steve Miller's Liaden Universe aren't really morons per se, so much as they appear to be large and slow, with a child-like innocent naivety regarding human culture. But those who get on their bad side discover, very briefly, the error of their ways.
Their space drive could be considered a metaphor for the Turtles themselves: normally slow, quirky, and meandering, it can move very quickly and directly if the Turtles see sufficient need.