Raiha and Joker in Flame of Recca. Kurei even compared Raiha to a Japanese warrior who pretended to be an idiot, to make others underesrimate him.
The titular character of Irresponsible Captain Tylor, who constantly kept everyone (including the audience) wondering whether he was a tactical genius or just incredibly lucky.
There are strong reasons to think (and many fans do so, indeed) that he actually is an illuminated bodhisattva. If this interpretation is correct, the surreal opening animation actually shows the moment of his Buddhist epiphany, and Tylor's real ultimate goal all along the series would be to bring enlightenment to his crew. (Especially to Yamamoto, an impressive success!)
Himura Kenshin in tried to pass himself off this way in the first episode, but was eventually found out. He continues to act like an idiot whenever he's not fighting at least for the first half of the series. He usually manages to maintain the masquerade until someone familiar with his past tries to force him to fight properly.
The puppet master Gein also plays to be really stupid as his alter ego Iwanbō.
Genma Saotome from Ranma ½. He behaves like a lazy, thieving, sadistic, cowardly, gluttonous, etc etc and a total waste of space. And maybe he is. But the one time Ranma seemed about to outpace him, Genma asserted dominance over Ranma with psychological attacks (the "Hell's Cradle Technique"). Also, Genma managed to create two new martial arts forms from scratch that would be at home in the Dragon Ball stories, and once managed to prove himself the near-equal of his evil master Happosai by manifesting Godzilla-scale powers for a brief moment.
Lt. Colonel Hughes hides his deadly skill with knives and investigative intelligence behind a public persona of a ditz who's always shoving pictures of his daughter in front of anyone and everyone. Or maybe he just is a ditz who adores showing pictures of his daughter and is an awesome investigator at the same time. In the Brotherhood OVA, he reveals that part of why he created this persona is because he doesn't want to burden his family with what happened in Ishval.
To an extent so is Major Armstrong in the anime, though he hides his intelligence and investigative skills behind a meat head persona rather than the classical ditz. His tendency to rip his shirt off at every opportunity is more an aspect of his personality.
Fuhrer King Bradley beats them both, though, especially in the manga. While those who served in the Ishval conflict know or at least have a hinted clue just how vicious he can be, he starts out being presented to the audience and the two protagonists as being a harmless kook who likes avoiding work and giving people melons as gifts, which makes the revelation of his true personality and the combat skills that go with it that much more terrifying. There's a very, very good reason why his other name is Wrath.
Roy Mustang. A good-looking soldier, who only cares for promotions and has sworn to protect his comrades and underlings using his position and power. He dates several girls at the same time, using this so that people wouldn't notice him too much. He constantly goes to a brothel/pub with a lot of girls, (to gain information from the girls. Also, the pub owner is his mother. He uses military phones to call his girlfriends, in order to direct the 'girlfriends' in coordinated attack. Finally, his assistant has to keep him in check, read: stop him from going too far with/away from his idealism. Sounds like a bastard, doesn't he? Good thinghe isn't.
In truth all soldiers in Mustang's group except Hawkeye (who doesn't hide her smarts) are eligible, because every soldier in FMA has a mask.
Ling Yao is sort of like this, although his undignified goofiness does seem like a natural part of his personality that he just deploys strategically. He first appears as an obnoxious, greedy Funny Foreigner who tries to weasel his way out of paying for damage he himself caused ("So sori, I no undastand much language of zis countri, bye bye now!"), and then he pulls out his sword and hands people their asses. He even manages to survive a fight with Wrathwhile carrying an injured Lan Fan.
Edward Elric himself. He acts like a hot-headed moron, and is especially stupid at times, but then he figures out something that men twice his age couldn't do, passing the State Alchemy Exam at 12, which normally takes up till the age of 20, and learning how to do Human Transmutation.
The man who taught Mustang some of his Obfuscating Stupidity, Lt. General Grummon. Hiding behind that chess loving, female officer harassing, general funny old man personality, is the mind of a cunning chessmaster.
Xellos tends to give an impression of amusing if annoying harmlessness as long as his eyes remain closed, hiding his true, sinister nature.
Gourry himself would be the textbook example, especially in the original novels, where he's a Deadpan Snarker who likes to pass as a Dumb Blond for fun and profit. In the anime — not so much. Though he still get some good moments.
The inspector in Slayers Revolution seems to be approaching Too Dumb to Live territory in the beginning, until it is revealed that it is all just an act to capture his real target.
Lina could arguably be this since her general status is twelve steps ahead of everyone or not. The "or not" usually happening because she doesn't actually care about the situation involved. However, it's hard to tell which is the case since her general behavior doesn't change at all between being in left field or out-chessing everyone else.
In his first appearance, Kakashi "falls" for Naruto's juvenile prank, making his charges think he's a moron. Of course, he proves them wrong later in the episode...
And while that put him out of the "stupid" category, Kakashi's next four opponents (counting Haku, who observed and tried to deconstruct his fighting style so that Zabuza could later kill him) all fatally underestimate him in three different ways, just to drive the point home that Kakashi has whole layers of this going just by force of habit. Given that Kakashi is fairly infamous among Konoha's enemies, the fact that he's still able to get enemies to underestimate him is rather impressive.
There's also Shikamaru, who's a borderline case. He really is smart, and when he wants to buckle down, he's an unparalleled strategist, but he's extremely lazy. According to his sensei, Asuma, he felt that even moving his pencil in his class was too much trouble. When Asuma got Shikamaru to play a game that was actually a hidden IQ test, he discovered Shikamaru has an IQ of over 200 (for comparison, Albert Einstein had an IQ of 186, which made him smarter than 99.9999% of all humans). Still, a standard battle involving Shikamaru usually plays out like this: Shikamaru gets his ass handed to him for 95% of the battle, and just as the enemy is about to close in on him, he reveals that he's known their plan all along, and was just messing with them.
Tobi, the Akatsuki's comic-relief member, has been using this tactic since his first appearance. He's really Obito Uchiha, the former teammate of Kakashi, and both The Man Behind the Man and Big Bad to boot.
Rock Lee's debut featured him also pretending to be an inexpert rookie moron so Team Guy can go around before the Chuunin exams without standing out. But when a fight breaks in, Lee can't help himself and promptly stops the fisticuffs, leaving everyone surprised at how an apparent weakling was so skilled.
To a lesser extent, Lee's teammate, Neji. Though an Arrogant Kung-Fu Guy (to the point where he's practically the Trope Namer) in his early appearances he hid the fact that he had managed to master many of his clan's most advanced techniques and even improve on them, just on basic theory alone.
Jiraiya definitely displays this trope. At the start of battles, he acts like an idiot and makes great, unneeded moves, to throw off the enemy to underestimating him. When they attack...he attacks with utmost seriousness to put them down in the most efficient way possible. Outside of battle, it's hard to take him seriously due to his perverted actions and his tendency to hang out in the Red Light District. As it turns out, a large number of contacts in his spy network can be found in said districts.
Pegasus feigns intimidation and hopelessness when Kaiba duels him, and as a whole comes off as a real goof who has trouble taking anything seriously. The reason he acts this way is to keep his opponents off-guard when he reveals himself as a master duelist (he is the guy who made the game after all). It is also implied that Pegasus might act like this just because he knows it annoys people. Even if people don't buy the act, the annoying part works perfectly. His deck is the same way, consisting of comical over-the-top "Toon" monsters that chuckle and make faces while attacking. Just watch.
Mai also makes use of this trope. Pretending to be a Brainless Beauty and Fangirl, she challenges Rex to a duel; if she wins, she gets his room. If he wins, he gets to spend the night with her. Severely underestimating her, he accepts her challenge. Some pages later, she kicks him out of his room.
Dark Magical GirlNinja (yes) Freesia Yagyuu of Jubei Chan hams up her Half-Russian heritage with broken Japanese and a vapid demeanor. In reality, she speaks perfect Japanese, and is frighteningly intelligent.
Kumiko from Gokusen swings back and forth between The Ditz and the Action Girl as a scene requires, even throwing in a little Clark Kenting to clue the viewer in as to which one she's trying to be.
Rika Furude is proven to be this in season 2, though in the original Visual Novelher intelligence is hinted at much earlier in the TIPS.
Also, Rena gives off the clumsy, ditzy feel, but she may just be the smartest of the gang. She shows incredibly, almost absurdly, good detective skills when Satoko and Rika disappear in Watanagashi-hen and made up an almost believable theory about Hinamizawa in the Atonement chapter...until she lost it and started talking about aliens.
Keiichi is also an example of this as before he moved to Hinamizawa he was an Insufferable Genius with no friends that was picked on constantly in school (which lead to his unfortunate stress reliving activity). After moving he decided Dumb Is Good and began acting like he is known for in the series; however his intelligence sometimes shines through his act and he appears simply Book Dumb. And he's not Book Dumb at all. Several scenes show him tutoring the others, including the older Mion, and it's implied he gets the best grades of the group. He has learned by the start of the story to not put on an act just to feel good about himself and impress others, so he acts the way he does because that's how he genuinely is. So it's really more like he completely lacks common sense. Given the setting, he fits in right in right away.
Another shonen protagonist of this persuasion is Taikoubou of Houshin Engi. In almost every situation he adopts a manner that is either agonizingly lazy or comically bizarre, but he is in truth an adept and cunning tactician.
Ichigo's father seems totally oblivious to the fact that his son has become a Shinigami, regularly leaves his body to go fight hollows, and has had up to four sentient stuffed animals in his room, in addition to having a girl living in his closet. We then find out that Ichigo's father is actually a Captain-level Shinigami himself, and was fully aware of his son's exploits.
Ikkaku passes himself off as a third-seat shinigami, but hides bankai. Edorad observed that he throws away skill in battle to fight purely on luck. He's a much better, stronger fighter than he wants to admit and the only reason he isn't working to become a captain is that he doesn't want to leave Kenpachi's command. He even trained Renji to achieve bankai.
Yumichika is only fifth seat, right? Except that he refused the fourth seat because he doesn't like the number four, he "let" Ikkaku have the number three, and most importantly of all, he's never used anything more than a weak, crippled version of his true shikai in public. Kubo himself has stated that he's actually Ikkaku's equal in strength - quite a mask in a world where power levels and rankings are constantly monitored and compared.
Urahara puts on the personality of Mr. Hat and Clogs, an eccentric shop owner, to cover for his real self, a ridiculously skilled scientist and inventor and a former Shinigami Captain. He's been at it for over a hundred years but he used to be the warden of one of Soul Society's highest security prisons which required him to be able to take down/overpower prisoners with his bare hands.
Squad two lieutenant Omaeda - who looks and acts like an Upper-Class Twit - fights against one of Barrigan's fraccion. During the fight, he manages to use his apparent stupidity to trick his opponent into using his resurrection ability, then demonstrating exactlywhy he's second in command of what basically amounts to the Soul Society special forces.
Pesche and Dondochakka might count too - despite their usual goofy behavior, they were Nel's fraccion back when she was the 3rd Espada, and claim to have been training even further since then. Szayel even admits that their Combination Attack would have killed him if he hadn't had a chance to analyze their powers beforehand.
Captain Kyoraku a womanizing goof who'd rather drunk and sleep than fight Chad who casually No Sells everything Chad throws at him, and his best friend Ukitake who after waking up from being ill and finding out that soul society is under attack stops Knight Templar Byakuya with no effort. Then they up the ante by tag teaming Yamamoto (their commander) and later on facing down Coyote Staark and his fraccion Lynette who just so happen to also be the strongest Espada and their arrancar counter parts. Behind their easy-going natures lie two of the first captains promoted by Yamamoto.
Kenpachi Zaraki carries Yarichu everywhere. She nicknames everyone she sees, wants nothing more than "Ken-chan" to fight and for a good while she looks like his Morality Pet. Then someone tries to give her a message when she's watching Kenpachi fight Ichigo and makes him crap his pants. And goes straight back to being a harmless innocent girl for the rest of the series...
Haruko Haruhara from FLCL uses the façade of a goofy policewoman from space so that no one questions deeply what she's doing here in the first place and what her goals are. In the last episode she finally reveals what she was planning, to absorb the powers of Atomsk, the Pirate King. She almost succeeds, too, but Atomsk eventually escapes, so she leaves to pursue him again.
Or something. It's not like you really understand what she wants after watching the show.
In Idaten Jump we're introduced to Arthur, a mild-mannered and geeky-looking painter with Nerd Glasses who enters the MTB tournament and becomes a Butt Monkey among fellow competitors. It turns out that Arthur is not only a very handsome blond, he's an excellent biker and a good friend of the local Wrench Wench Yuki, who pretended to be dumb to hide his identity as a member of the guerrilla against Gabu, the child dictator and leader of the Shark team.
He's a lazy, tanned Buddhist monk in his late 30's with a stubble, whom his wife treats like a younger brother and his kids (both 12-year-old son and 19-year-old niece) treat with not too much respect, and who often ogles attractive girls much to others' embarrassment. But give him a racket and/or bring him to a tennis match...He'll either beat the crap out of you at the courts or give you the most acute comments about the current game. That's Nanjiroh "The Samurai" Echizen from The Prince of Tennis to you (as in the title character's dad).
One early look at Mai-HiME's Midori Sugiura would likely lead one to think: "Clumsy waitress...ditzy teacher...I could probably take her in a fight". However, once she gets into her Element, she can (and will) kick ass with flair, occasionally exhibiting leadership qualities that would make Storm proud.
In Full Metal Panic!, Melissa Mao reflects back to her initial encounters with Sousuke and Kurz: she was sent to scout the training camp they were in for candidates to recruit to Mithril. Both Sousuke and Kurz, mistrustful of the mysterious organization sponsoring their training, deliberately underperformed: Sousuke was content to maintain a level of careful mediocrity, but Kurz went the extra mile and staged an attempted sexual assault on Mao to make sure she'd strike him from her list. When a mission came in and most of the other members were captured, however, both of them were obliged to demonstrate the full level of their considerable skills.
Gauron is lampshaded to have the habit of doing this to fool his potential prey...at least temporarily, before his psychotic, Ax-Crazy tendencies take over. As Kalinin described him in Kyokuhoku Kara no Koe, "When you were fooled by his seemingly languid appearance, he would suddenly display his determined and violent nature."
Thorkell in Vinland Saga has such a goofy grin on his face most of the time you can easily forget he's a killing machine. That, and his good-natured ribbing of both friend and foe make him come off as downright harmless. Until he splits a man in two with a single blow, or crushes a guy's skull for speaking out of turn. Just look out if you make him really angry, 'cause he will punch your horse to death. Yep, a bag of laughs that Thorkell.
And then we have Jack Rakan. Sure, he's powerful, but he's just a overly rambunctiousskirt-chaser underneath all the muscle, right? Wrong. So, so wrong. That happy-go-lucky attitude is born from the fact that he's been involved in brutal, life-or-death combat for over forty years, so he can afford to act goofy because there is honestly nothing that poses a serious threat to him at this point. His actual intellect is shown off fully in the magical world tournament: after Negi develops a technique that literally let him turn into lightning, increasing his speed to unbelievable levels...it takes Rakan exactly one observation of said move to analyze it, find all the flaws, and devise counter-techniques which allow him to effortlessly and utterly kick the crap out of 'invincible thunder god Negi'.
Kyon in Suzumiya Haruhi (Much more obvious in the light novels) often appears as a Book Dumb student no better than a janitor. Granted, he cannot comprehend Koizumi's theories (Can you?) or Haruhi when she's at deducing and solving math problems. He doesn't even want to listen. However, he usually knows exactly what's going on, especially if it comes to figuring out other characters' hidden motives and feelings. Being the Unreliable Narrator he is, he may even fool the reader. Also made more clear through Little Professor Dialog; he drops a suspicious number of references to concepts he claims to know nothing about.
To quote the man himself, when he alone solves the fake murder (In the novels):
Kyon: "And I may not look like it, but I do pay attention to things that matter. [...] Don't underestimate me."
It's strongly implied (throughout the anime, at least) that he's just too lazy to act smart.
The whole SOS brigade sort of counts here. Kyon suspects Koizumi of doing this; Koizumi suspects Mikuru of doing this. And no-one outside the brigade pays much attention to Yuki, just sitting in a corner reading.
Suzuko Tashirou aka Norie Otobe from Glass Mask. Who would think that the nerdy girl with glasses and a Kansai accent would be such a cruel Manipulative Bitch, able to play a frighteningly good plan to have Maya Kitajima kicked out of the acting scene? Unfortunately for her, Maya's rival Ayumi Himekawa was NOT amused when she found out...
Mrs. Ketchum (Ash's (hot) mom) in Pokémon is another borderline case. She's been a single mom for as long as the anime has been on the air, but it's later revealed she was a student of Professor Oak's, and an exceptional one, at that. Chances are she just comes off as uninformed since she had to put her studies, and such behind once Ash was born.
Kenichi of all people pulls this off in chapter 307. He already figured out that Kushinada is a member of YOMI. He's trying to win her over without a fight because he Wouldn't Hit a Girl.
Also in Kenichi: The Mightiest Disciple, there's Apachai Hopachai, who despite his childish personality, can and HAS murdered dozens of people with his bare hands, being a master of Muay Thai. In fact, it has been explained that he completely lacks the ability to hold back, and striking with lethal force is reflex for him. He may act like a baby, but hope to God that you don't find his Berserk Button.
He's never actually killed anyone, though. Well, unless you count Kenichi (by accident).
While setting to rescue Miu, Kenichi and Sakaki meet John, an overweight mercenary who gives them aid until he reveals himself as Furinji Saiga, who is also Miu's father and YAMI's leader
Bit Cloud, of Zoids: New Century Zero makes it hard to tell whether he's a Bunny-Ears Lawyer or Crouching Moron, Hidden Badass or even Idiot Hero, but the most common diagnosis is Obfuscating Stupidity. Interestingly, his guise is to act as a Genius Ditz, with the incredible knowledge of Zoid parts and mechanics a scrap merchant should have but without the practical knowledge to survive a more difficult fight or even the complexities of living in the same building as the TsundereGirl with Psycho Weapon. Then he starts beating skilled opponents through complex strategies like wasting ammo on a cliff face to force a long range focused opponent into mêlée, and he starts looking practical in battles through luck or otherwise, even if he'll eventually find himself on the wrong end of a Weasel Total Assault. Then the team's tactician realizes that said Tsundere only fights best when firing missiles at wherever Bit is standing.
Nineteen-year-old Emperor Shi Ryuuki in Saiunkoku Monogatari is initially called "stupid emperor" by members of his court disgusted by his complete lack of interest in ruling his empire, and his habit of spending his days hiding from court officials and spending his nights sleeping with other men. When properly motivated, however, Ryuuki reveals that he has a much defter hand for political intrigue than anyone suspected, and that there's a very good reason that he is the only one of six brothers to survive the imperial court long enough to take the throne; he cultivated the "stupid emperor" image as a survival mechanism, and refuses to rule in the hopes that his exiled older brother Prince Seien will return to take his place.
After Shuurei convinces him to get serious about governing Saiunkoku, Ryuuki keeps playing the idiot so that she'll stick around for a while longer to tutor him. As you can imagine, Shuurei is furious when she finds out.
Conan of Detective Conan repeatedly makes a very awkward use of this to disguise his investigations and artificial Creek Moments. In general, he gets away with it more because of him looking like a child than his questionable acting skills.
Also, Jodie (the undercover FBI agent pretending to be a teacher) pretends to be far less fluent in Japanese than she actually is; Heiji picks up on this and calls her out on it.
Eisuke Hondou, while genuinely clumsy, has exploited this weakness to obfuscate some of his scooping behaviour.
Dr. Shamal from Katekyo Hitman Reborn! comes off initially as being a rather ditzy, womanizing lech that is completely incompetent. And then it's later revealed that he's strong enough to have managed to inject a virus into Hibari at the exact same moment Hibari hit him without Hibari even noticing.
Rokudo Mukuro also does this to some extent during his first meeting with Tsuna, pretending to be a helpless boy who was captured by...Rokudo Mukuro.
Tsuna's father Iemitsu Sawada came across as a loving husband who spent all of his little time time home eating, drinking, and sleeping. He's Vongola 9th's chief advisor and implied to be a powerful mafioso. Later in the Curse of the Rainbow Arc he used Tsuna's perception of him as a ditz to throw Tsuna off balance and defeat him.
Dr. Stein from Soul Eater plays this trope during his first appearance and meeting with the protagonists. The way he appeared didn't exactly impress them, rolling his chair backwards out the door and falling over. And then doing it again. Of course, he turns out to be a super badass with sadistic tendencies.
He plays with it throughout the series, really. Any time his glasses are perfectly opaque and round (not to be confused with shiny) a la Nerd Glasses, the next words out of his mouth are probably going to be interesting, if not downright dumb.
There's also Shinigami. At first, he seems like a fairly silly Dumbledore-esque teacher, which clashes with the fact that he's, you know, Death. And then you meet his Scythe, who is a womanizing twit who spends his time alternating between patronizing a whorehouse and crying over his estranged daughter, and it all seems to make sense. And then, several chapters later, once you've gotten acclimated to the idea that Shinigami is a silly old fool long past his prime, we realize that he once imprisoned an insane subordinate/disciple by ripping off the guys skin, turning it into a bag, and imprisoning the guy's body in it, and is perfectly willing to do it again once said guy escapes. And if the latest chapters are any indication, he's a full-on Eldritch Abomination as well.
It's stated that he puts on that facade so that he doesn't freak his students out
Prince Parion of Orguss 02 feigns idiocy for the first few episodes of the OVA - until he orchestrates the murder of his half-brother and the Evil Chancellor who killed his father, assuming the throne himself. He then goes on to attempt a global takeoveromnicide using a Humongous Mecha.
Czeslaw Meyer from Baccano! does a bit of this, deliberately playing up an Adorably Precocious Child image, to mask or downplay the fact that he's at least two hundred years old ("What? Did I just say something that wasn't very child-like? You must be thinking too much").
Later novels suggest that maybe, just maybe, Isaac and Miria might be playing up their legendary stupidity.
Ukyo in Samurai 7 seems an idle, childish, vain hedonist...and he is, only he is also brilliant enough to successfully earn the right to be the Emperor's heir when all the Emperor's other clones had failed. Clever enough, ruthless enough, to assassinate and usurp the Emperor afterwards, and no one suspects him.
Commander Doolittle in Mars Daybreak comes across as being either extremely lazy, extremely incompetent, or both. However, he comes the closest to actually trapping the Ship of Aurora, and didn't need an entire fleet to do it.
Ma Gangryong from Veritas spent his first few weeks at Ninja School mouthing off to people stronger than himself, and then getting beat up. He later reveals that he mouths off because it makes the highly refined fighters around him angry, and thus sloppy, which is his style. He also points out that after having lost so many fights, everyone thinks he's weak, and that they'll continue to think so long after he's surpassed them.
In One Piece, Luffy does do some pretty silly things once in awhile (OK, almost all the time), but he has shown an amazing insight into certain things. Like with Alabasta, he pointed out that in order to stop the rebellion, they should stop Crocodile and not the pawns that he tricked into rebelling. Then, at Thriller Bark, with some of the crew having lost their shadows and worried about confronting their own shadows, Luffy simply reminded everyone that by beating Moria, everyone's shadows will come back. Which also sorta counts as When All You Have Is a Hammer since he's pointed out that all pirating skills are beyond him, he just has to be able to apply his one skill the best: beating the crap out of the strongest guy who happens to be in their way.
Maybe his simple mind lets him see to the heart of things. I don't know.
There has to be some reason that he's still the captain, when he's obviously surrounded by people smarter than him.
He's a pretty good judge of people as well. And while he may be less smart than anyone on his crew, he is perhaps the wisest of all of them. Luffy's simplest outlook on life allows him to see things as they are without the complexities muddling everything up for him, so while his crew may be trying to figure out a personal problem with all the complexities in mind, Luffy's the one who usually points out the simplest and most logical solution.
Probably the earliest example of how intelligent Luffy can be is when the Going Merry is about to crash into Laboon (the insanely huge island whale) at the bottom of Reverse Mountain. While the others are trying (ultimately in vain) to steer around it, Luffy goes below deck and uses the cannon as a retrorocket. So instead of smashing the boat to bits, the only thing that breaks (unfortunately) is the figurehead...his "special seat".
Zoro too has his moments. Usually, he's seen sleeping, drinking or off fighting. But at Alabasta, he was the one who thought of the white bandage for them to separate them from the enemy. But the real brilliance comes when there was a symbol of an X underneath the bandage. If one of the enemy pretending to be them can't do that, then they would know it's the enemy. Even Sanji calls him out on it, thinking that it was a little suspicious that someone like Zoro was able to think of something so clever like that.
While Luffy and Zoro more have screwy personalities that make it seem impossible they actually possess any form of brain, Sanji perhaps is the only one who puts on the stupidity intentionally. The best strategical mind on the Strawhats, he often looks just far enough ahead to pull a vital string that ends up saving the lot of them down the line. See in Water 7 when he realized Robin would be leaving via sea train and ran off early to stow away when everyone else was still messing around trying to figure out what to do. Ask him what he was doing beforehand? He has to go "see about a lady". Faced with the second best fighter in Croc's posse, and confronted as to whether or not he was the code-named orchestrator of the Straw Hats' escape? No, he's "just a simple sea cook." He stays out of sight, doesn't give his name, acts like an idiot (except in regards to his nature as a Chivalrous Pervert; that part isn't an act) and generally ends up, as Zoro pointed out mockingly, in the convenient position of being a Badass (Zoro left that part out) who everyone takes to be "pirate A" That does have the unfortunate side effect of his bounty poster though.
The best example is when at the climax of the Enis Lobby fight Sanji disappears in the middle of a melee against captain and vice-admiral marines for several chapters. When he comes back Zoro chews him out for ditching them in the middle of the fight. When they try make their escape and are chased by the 9 other warships it turns out Sanji sabotaged the gates of justice to allow the straw hats out while everyone else had been busy enough with "focus on surviving at this moment"
it becomes a running gag for Sanji to go under the radar as his wanted poster looks nothing like him and no one believes that he is Black Leg Sanji of the straw hats.
Speaking of Water Seven, its mayor, Iceberg, put on a good enough show of Obfuscating Stupidity that the arc's villains, spies who had been stationed near him and included his secretary and two of his most trusted shipwrights, couldn't muster the confidence to make an overt move for five years, when their deadline forced them into action.
Blackbeard in keeping with his Dark based powers prefers to stay out of the spot light for the most part. When he makes his entrance however he quickly becomes one of the 4 Yonko.
In Axis Powers Hetalia, during the WWI scene, Germany thinks that North Italy is trying to use this on him. He's wrong, because North Italy really is The Ditz.
True, Italy is The Ditz, but he's also hundreds of years old. He actually did invoke this when he was a kid, pretending to fall for a rich man's bribe of candy but then denying him what he wanted anyway.
Actually, most of the Hetalia characters are probably this in some way. France acts llike a narcissic flamboyant pervert most of the time, but he's been shown to have Hidden Depths. America can't read the atmosphere, but he does so intentionally - he could if he wanted to. Spain is a clueless dork, but has a scary side to him.
Hellbat in Transformers Victory acts like a devoted and none-too-bright servant, but is in reality is waiting for just the right moment to overthrow Leozack and Deathsaurus. Since Leozack also wants to overthrows Deathsaurus...
Most of the time, Shigure from Fruits Basket seems to just be a lazy, lecherous idiot of a novelist whose hobby is playing evil pranks on his poor editor in order to avoid his deadlines. As a matter of fact, it turns out he was actually a Manipulative Bastard all along. And possibly also a lazy, lecherous idiot. His acting is so convincing it's tough to say just how much of it was Obfuscating and how much was real.
Seems more like it's a split personality style (the anime at least)
While not as intelligent as Magnificent Bastard Light or Guile Hero L, Misa Amane of Death Note is smarter than your average blonde ditz. Although her impulsiveness almost gives her away and irritates Light, she did take reasonable precautions in an attempt to not leave evidence and is even arranges the meeting between her and Light right in front of L's nose. She even realizes that Light doesn't love her and that he is using her and will possibly kill her, she just doesn't care; unlike the calm and collected Kiyomi Takada.
Sakamoto Tatsuma from Gintama appears to be a fool almost every time he is on screen. But how can that be, when he is one of the most successful businessman in the galaxy? Not to mention that a flashback shows him to be a serious, intelligent former resistance fighter.
Pokémon Special's Mr. Berlitz commissioned Ignor and Phool to watch over Platinum, who mistook Diamond and Pearl for her bodyguards (I&P were supposed to be the bodyguards in the first place). Given their antics in the time you see them, coupled with their names being variants of the word "idiot", you'd think Mr. Berlitz was an idiot himself for entrusting his daughter to these two. Per this trope, looks belie talent, and the two are very capable battlers with their Burmy and Buizel, as Saturn had the misfortune of discovering at the Lost Tower. They initially appear to have their asses handed to them by Saturn (who isn't even actually there, using a device to watch the scene and command his Pokemon) when Burmy gets its coat knocked off and Buizel appears to be abandoned, but it was all part of the plan as Buizel used its tail to create a whirlwind of Burmy's leaves to block Saturn's camera. Effectively blind, Saturn can no longer command his Pokemon which then get taken out in one hit.
Ruby is a terrible battler. When people are watching. Sometimes Ruby's damage control isn't thorough enough. Mr. Briney fully assessed the damage done to a Corphish that boarded his ship after he recovered from a bout of unconsciousness, and came to judge Ruby as a seasoned battler...only to dismiss those claims when the poor boy heaved over the edge of his ship. Then again, he's the "don't ask, don't tell" kind of guy. Then there was the girl caught in a herd of frenzied Grumpig that Ruby and Nana (Mightyena) shut down swiftly and efficiently - unfortunately for him, there wasn't enough time for him to cover up the damage before she pieced it all together...and even if he could cover it up, there was no way he was going to fool Sapphire.
Sapphire: Any trainer would have sent his Pokemon leaping in, but no! Every attack hit those black pearls dead-on. That's not an attack by an ordinary trainer... Ruby: That's strange, Nana. What came over you? Sapphire: Cut the act!
Rio in Spiral seems to be a ridiculously cute Dojikko, but she's as good of a Chessmaster as all the other Blade Children, if not better. And has the same obsession with bombs.
A lot of characters in Durarara!! but the one guy who stands out of all people is Ryugamine Mikado. He seems like your typical Naïve Newcomer, right up until he demonstrates that he's successfully weaponized 4chan. If even then, he still doesn't seem all that scary on a personal level, just wait until he starts stabbing people with pens with a horrendous expression on his face.
Grenadier - Though Rushuna comes across as The Ditz most of the time, pay attention to her more vapid remarks, then note how they all lie completely at odds with the competency she shows in other respects. She knows mathematics, in a society where educating women seems to be a fairly low priority, especially in such abstract concepts. She has a solid understanding of various general models of guns. Her analytical abilities are nothing to scoff at. She goes from laughing to serious as immediately as the situation demands. From that, it's easy to see that she's only pretending to be a scatterbrained bimbo, and her ditzy comments suddenly take on a new, very sarcastic meaning.
In the series Monster, we have Grimmer. Best shown right when first meeting the character, where he gives money to a swindler and, when someone tells him that, saying he never even noticed. Just a few scenes later, you'll find out he is much more well-informed than he appears to be.
In Dragon Ball GT, the evil dragon Naturon Shenron at first seems to be the most foolhardy of the the Seven Shadow Dragons, even seeming easy to defeat by tricking him into blasting himself. However, it turns out that it was just an act and that he's a lot more intelligent (and speaks a lot more sinister). He even pretended to be defeated as a means to trick the heroes so he could absorb one of them and become more powerful.
In WORKING!!, Aoi's behavior makes her seem to be very "out there", but she appears to be very smart and focused when you least expect it—for instance when countering Souma's attempts at blackmail.
In Read or Die Yomiko aka Agent Paper acts very clumsy, carefree, and childlike even in the heat of battle, but when finishing off her opponents, she lets loose some glimpses of her badass side.
The main character of The Legend of the Legendary Heroes, Reiner Lute, is shown as a lazy, failing student in the Roland Magical Academy near the beginning of the anime. This lazy facade is in fact, merely a method that allows him to hide that he is in fact, the single most skilled Magician in all of Roland and the fact that he possesses the Alpha Stigma, a power that allows him to copy any magic that he sees, and that, when he is put under severe emotional strain, pushes him into a Superpowered evil state in which he is easily able to slaughter fifty enemy Magic knights without even breaking a sweat.
Xerxes Break, in Pandora Hearts, may be an example of this. All the crazy quirks are absent in the flashbacks, and seem to disappear when he gets serious.
Isis of Magical Record Lyrical Nanoha Force, who initially looked like an ordinary clothes merchant who naively decided to help Tohma and Lily on a whim without fully realizing the level of danger she's putting herself in. Then we learn that it's just a facade she's using to hide her real identity from the TSAB. While there have yet to be a full reveal on just what she really is, we do know that she is a very powerful and skilled individual, to the point that the Huckebein deemed her as the biggest threat in Tohma's entourage.
Toru Nanamine in Bakuman。 acts like an overly enthusiastic manga newbie and breaks the rules by submitting it online. He apologizes and deletes it, but it all furthers a multi-layered plan to draw attention to himself, enabling him to show his next piece to the editor in chief himself and get some people to give him feedback on his work as part of his plan to get serialized as quickly as possible.
The title character in The Legend of Sun Knight is terrible at swordplay. He spends most of his time getting stabbed, spouting inane platitudes about the God of Light, and keeping up with his beauty regimen. Luckily for him, he's also a naturally talented mage, assassin, and necromancer, who shows signs of being a capable Chessmaster when he's backed into a corner. He was trained to play the part of the angelic ditz because it's good politics and PR.
Punie Tanaka of Dai Mahou Touge acts like a ditzy schoolgirl, until it's inconvenient. Then the smile goes, the high-pitched voice goes, and suddenly the ruthless queen-in-training emerges. This is the point when you should run away.
Lacus Clyne from Mobile Suit Gundam SEED comes off as an especially ditzy version of The Ingenue in her first appearance, and is so seemingly innocent and naive that's it's rather horrifying. In truth she's a Guile Heroine, Chessmaster, and political manipulator of the highest calibre, and is probably the smartest person in series barring only Big Bad Rau Le Creuset.
This comes into full play in the sequel when she organizes her own third party superpower called the Terminal, have them create insanely powerful mobile suits that she gives to her friends, and then uses them to become the core fighting strength of the Three Ships Alliance. She goes on to face series Big Bad Durandal in Xanatos Speed Chess for the rights to control mankind's future, and once she wins, she becomes part of the ZAFT supreme council, possibly even the chairwoman, meaning that two twenty year old girls, her and Cagalli basically control the whole world and its colonies. And if you have any opinions about that, they could easily wipe you out by sending out those insanely powerful mobile suits piloted by their boyfriendsnote As a bonus, Kira is also Cagalli's twin brother and Athrun is Lacus's ex-fiance and childhood friend, reducing chances of them betraying the two girls to near zero.. Fortunately, they are the good guys.
Medaka Box: Medaka's older brother Maguro often acts like a perverted sicko who has a bit of an obsession with his sisters. But he's also incredibly intelligent, a master researcher, and well aware of the strengths of his allies.
In Tiger & Bunny, there are hints that Kotetsu exaggerates his klutziness and incompetence as a way making it easier for people to disregard him (and thus keep them from getting too close to him and worrying about him). Word of God confirms this.
The anime version of Wandering Son implies this with Chizuru, while the same scene in the manga just shows she can be something besides an outlandish Cloudcuckoolander.
Kami does this when he possesses a human in Dragon Ball. He poses as an incredibly dumb and very lucky fighter during the third tournament storyline, but reveals his true colors while fighting Yamcha.
Roberta of Black Lagoon is definitely this. No one would expect the maid that just burned supper to be an ex-FARC assassin.
Eikou no Napoleon-Eroica we have the title character, Napoleon Bonaparte. His insignificant looks, initial poverty and inexperience with women and politics are genuine, but he uses them to appear much stupider and weaker than he is, only to suddenly show exactly why he was promoted from captain to brigadier general after his first real battle. The best example of this is at Austerlitz, where he plays the tzar Alexander I, the Holy Roman Emperor Franz II and all their generals like fiddles by feigning weakness (to be fair, Kutuzov not only saw through the act but actually expected him to pull something like this, but was ignored and overruled multiple times), only to suddenly turn the tables on them and utterly and completely defeat the Austro-Russian army.
In the manga version of Sailor Moon, Minako. She is genuinely The Ditz, but exaggerates this big time to be underestimated (and for fun) and is by far the most battle competent of the Sailor Senshi. The only ones who actually know are Rei (figured it by the final arc, probably after wondering how the hell Minako was able to use her exact exorcism technique in the Exam Battle specials), the Three Lights (who actually call her out on this. Minako immediately dropped the act and threatened to kill them if they didn't drop theirs), and Artemis (who lives with her).