Liar Game: Nao. Like Corporal Carrot, she started off extremely naive, honest and easily manipulated. As the game continued, however, we see that she is a lot smarter than she appears. She even schemes with Fukunaga and doesn't tell Akiyama and pulled it off, and often uses her innocent nature to trick and trap others.
In Dragon Ball, Goku showed an unusual level of craftiness, and was shown to be at least reasonably clever. All of it outside of fighting. It seems he was just poorly educated.
In Dragon Ball Z: His eldest son Gohan is the kind of boy parents would love their daughters to bring home: nice, polite etc. He's also a full fledged Genius Bruiser who gets straight A's and smashes around beings stronger than the Gods themselves!!
Naruto: Sakura, Kakashi, Shikamaru. Just to name a few examples.
Souten Kouro: Cao Cao is serious about upholding the law, but he's not Lawful Stupid and knows a set-up when he sees it during his tenure as police chief. As he said in exposing the eunuch Jian Shi's plot against him: "I am not the kind of fool that would kill His Highness, who you had caught in your wicked scheme!"
Lacus Clyne of Mobile Suit Gundam SEED. One of the kindest and most forgiving people you would ever meet, and an Actual Pacifist. Do not mistake any of this for weakness or naivete. As of the end of Destiny, she is the Chairwoman of the PLANT Supreme Council, essentially in charge of one of the global superpowers of the Earth Sphere.
Hajime of Gatchaman Crowds is as optimistic as they come. While she does have one or two moments of Obfuscating Stupidity, most of the time she's completely sincere in how she acts, and she proves to be one of the most thoughtful characters of the series.
Minor character Marlow in Attack on Titan, while in-universe is seen as foolish for wanting to change things, he is definitely not stupid, able to make astute observations that others haven't noticed or chooses to ignore.
It's implied that The Gentleman from Astro City is one of these. His goodness is never in question — he's unfailingly polite, selfless, and idealistic, even in the midst of battle. On the other hand, his intelligence to date has been largely implied; for example, he's one of the few super-beings who avoided capture during a secret alien invasion.
Spider-Man certainly has his flaws, he's hot headed, neurotic and can occasionally descend into bouts of self-pity, yet he's still extremely loyal to his loved ones, lives by a very strict Thou Shalt Not Kill code and above all else, he values responsibility. He also happens to be a genius scientist.
In Zatanna's ongoing series she is confronted by Oscar Hampel, who claims that he was turned into a puppet because of a tragic series of events almost out of his control and that his violent actions were an isolated event. Zatanna accepts that her father, for all his wisdom and power, was only human and might have overreacted by turning Oscar into a puppet. She gives Oscar the benefit of the doubt and agrees to help him become human again...after she runs him through a magic Lie Detector, that is. After all, just because her father was not perfect does not mean he was wrong this time, and she is going to make sure before she takes any actions.
The dwarven noble protagonist in this Dragon Age fanfiction can be considered an embodiment of this trope.
The Reasonable Marines, a fanmade Space Marine Chapter for Warhammer 40,000, will attempt diplomacy first whenever possible, which makes then positively heretical in the shoot-first-ask-questions-never Imperium of Man. The fool that refuses their overtures gets to be on the receiving end of stealth tactics, combined arms and all-around Combat Pragmatism.
In 3 Slytherin Marauders Arthur Weasley came up with a diversion which made Lucius Malfoy wonder when he'd become so clever.
Abbe Coulmier from Quills is a compassionate priest who believes Rousseau Was Right, and serves as a foil to the Marquis de Sade. While it initially seems like de Sade has the advantage, Coulmier turns out to be more than capable of zinging him right back, and punctures de Sade's pretensions to evil.
"You're not the anti-Christ. You're just a malcontent who knows how to spell."
Georgia Byrd from Last Holiday might seem naÔve, but she is a very good saleswoman and gives some solid advice to other characters. Despite all of Kragenís attempts to humiliate her, Georgia is usually one step ahead of him.
In Cars 2, Mater's simple nature belies the fact that he's a genius at recognizing obscure car parts at a glance. He later uses this to identify Sir Miles Axelrod as the mastermind behind the efforts to sabotage the World Grand Prix.
Glinda the Good in Oz: The Great and Powerful almost immediately figures out that Oz is not a wizard. Still, she knows that people need to believe that he is the Wizard of the prophecy in order to win against the Wicked Witches. This is in sharp contrast to Theodora, who is completely taken in by Oz, who flirts with her just like any other gullible girl, to the point where she's planning a wedding after knowing him a few hours. She also completely fails to notice her sister Evanora playing her, resulting in Evanora turning her into an Axe Crazy Wicked Witch.
Carrot Ironfoundersson greets everyone by name, is perpetually polite and cheerful, and selflessly volunteers to help anyone in need. But anyone who mistakes him for an easy mark quickly learns otherwise.
And that was Carrot at work. He could sound so innocent, so friendly, so... stupid, in a puppy-dog kind of way, and then he became this big block of steel and you walked right into it.
While Sam Vimes is a textbook example of Good Is Not Nice, his wife Sybil is an example of this trope. She's always unflappably polite and kind-hearted (even to Nobby Nobbs), but beneath her lighthearted exterior is a razor-sharp mind, as demonstrated when she negotiated Ankh-Morpork's fat trade with the Dwarf King in The Fifth Elephant.
And then there's Nanny Ogg, the Cool Old Lady who's always up for a good drink, a good smoke, and a good ribald song. Yet she's smart enough to keep Granny Weatherwax in check...
In The Hunger Games, Peeta is kind and patient and totally kills people in the arena, including finishing off one girl in cold blood while he's in the Career pack, besides being three steps ahead when it comes to manipulating the on-camera narrative.
Well, he kills Brutus in the second arena. The girl he killed in the first arena was a Mercy Kill.
The Father Brown series by G. K. Chesterton uses this heavily with its titular character. In his first appearance, the Gentleman Thief Flambeau is shocked that a quiet, unassuming priest can not only outwit him but knows more than him about criminal behaviour. Father Brown points out that of course priests know these things; people confess to them.
None of the main cast of Codex Alera can be considered dumb, but Tavi in particular stands out. He's constantly derided for being overly idealistic and trying to make peace with nonhuman species who have been at war with Alera for centuries. However, he's a Guile Hero with a talent for Crazy AwesomeBatman Gambits and understanding creatures that don't think like humans, so as often as not his idealism actually pays off, much to the surprise (and sometimes annoyance) of his detractors.
Jim Butcher's other series, The Dresden Files, also uses this trope on the Knights of the Cross, Michael Carpenter in particular. Michael is a Church MilitantKnight in Shining Armor and devout Catholic, but he's also a perceptive person. If it looks like he's falling for a plan, it's because he believes it's the only honorable way to get Harry out of the latest mess and/or God will see him through it, never because he hasn't noticed the risk.
Also because Harry has risked the same for him.
When Harry receives the shadow of a Fallen Angel, he worries about telling Michael. When he finally does, Michael calmly tells him that he knew. Harry forgot that the Knights job is to help those who have evil within themselves redeem themselves.
Brother Cadfael from the Ellis Peters mystery novels is a very intelligent man, quite good at medicine, reading people and bringing the most unnoticeable clues together. He is also remarkably kind and compassionate. Hugh Beringar is also a good and honorable person — and a Magnificent Bastard on top of that.
In Timothy Zahnnovels, Luke is written this way. While he may be one of the strongest Jedi, he is also able to outsmart his opponents when necessary.
In The Lord of the Rings, Frodo makes it very clear to Gollum that he is well aware that Gollum is trying to think of a way to betray the hobbits and take back the ring. Sam is surprised at this because he had assumed Frodo was far too good a person to be able to understand deception and treachery. Sam admits that he (and probably Gollum as well) "had confused kindness with blindness."
Live Action TV
The Doctor on Doctor Who frequently makes use of this to his own advantage. Although his kindness is almost always geniune, it frequently earns the scorn of various despots, tyrants and baddies who assume him to be simple minded or naive.
Benton Fraser from Due South. Honest, noble, impeccably polite at all times... and a lot more competent and intelligent than he appears. Incredibly reminiscent of Captain Carrot, to the point that you think somebody must have been inspired by somebody else. Apparently not, though.
Dr. Molly Clock in Scrubs. Her cheery optimism refuses to yield even against the naked cynicism of Dr. Cox and Dr. Kelso, and allows her to triumph against them.
In "Trash," Saffron assumes Mal is an idiot because he's being kind and compassionate to her. Then she walks headlong into his Batman Gambit when it turns out he expected her sudden but inevitable betrayal, and Inara beat Saffron to the drop point.
In "Ariel" Simon—to that point seen along with his sister as The Load by the rest of the crew—comes up with a plan to steal medical supplies from a hospital. It's a win-win for the crew; they profit from the medicine (which they can sell on poorly-supplied colonies) while Simon gets access to diagnostic equipment he needs to help his sister. He specifically targets an Alliance military hospital for the crew's raid because he knows it will be resupplied quickly, thus not jeopardizing patient safety. He even breaks his cover to attend to a patient who is in distress and being ignored by the regular staff, and manages to (briefly) win Jayne's respect in the process. That still doesn't stop Jayne from selling him out, however.
Carly in iCarly sees the best in people, but if betrayed or oppressed, will come up with a scheme like having a massive in-school riot to get the good principal back.
Occurs several times in Survivor — Natalie in Samoa successfully played Russell's scheming to her own benefit. Also "Fabio" in Nicaragua, who had a "lovable goof" personality but was reasonably game-savvy and combined the two to get the win.
On Season 2 of The Amazing Race, Tara & Wil and Chris & Alex constantly ragged on Blake for being an idiot, despite this, he made several brilliant strategic moves, including being the first team to beg for money, getting his bags on a flight when all the other teams had to check theirs, and getting preferred parking on a ferry, most of which were decried by the above teams as "cheating".
Part of Boston Rob getting Uchenna & Joyce and Gretchen & Meredith on a faster flight in Season 7 (when Rob, in order to mess with their heads, mentioned a fictional earlier flight, which just turned out to exist) was him talking about how Uchenna & Joyce couldn't do anything for themselves.
Eiji Hino from Kamen Rider OOO may seem like a carefree fool, however underneath his simple exterior lies a rather cunning mind.
Arthur from Merlin may be the poster boy for "Genre Blind is not dumb". Even if he's convinced that Agravaine is innocent, he will investigate nonetheless, and came close to arresting him at least twice. He's also a very competent tactician, as you'd expect from the commander of an elite army, and, in more recent episodes, started valuing Merlin's advice above all others (although he'd never admit it).
Gwen as well. Compared to the other characters who frequently pass around the Idiot Ball, Gwen shows plenty of intelligence. For example, she spies Morgause talking to Morgana in the city and immediately goes to Gaius about it, as well as trying to figure out what she's up to. And when she becomes Queen and it's revealed that someone in Camelot betrayed them, she immediately puts two and two together remembering she had seen one of her handmaidens leaving the city late the previous night and is able to get the truth out of her almost at once, something Uther never really quite accomplished.
The Book of Exalted Deeds supplement for Dungeons & Dragons makes a point of saying, early on, that Good does not equal stupid. A Good character won't leave a village to be eaten by a dragon, but they're perfectly allowed to ask questions about its power, its minions, and where it's living - they aren't obligated to charge in blind.
Taken to the extreme in the Overlord DLC. When Shepard discovers what Dr. Archer did to his autistic brother David, s/he's reasonably pissed off, and takes David away to get treatment for the torture he's endured. When Dr. Archer brandishes a gun at Shepard, the player has the option to pistol whip him... as a paragon interrupt. The renegade option has Shepard leave David with his brother, but s\he still smacks him around and tells him he's a sick bastard who's only spared because the project might prevent a war.
Garlot of Blaze Union may not be very smart to begin with, but he has a very sensitive nature that allows him to accurately read and understand his rivals and enemies' motivations. As his adventures start to gain him more and more street cred, it's his overwhelmingly gentle and compassionate heart that manages to win the hearts of his entire country—including those very rivals and enemies, more often than not. We get to see in the future just how much Bronquia really appreciates having a leader who's kind, just, and competent.
Ashara Zavros in Star Wars: The Old Republic is the most blatantly Light Sided companion in the Sith Inquisitor's entourage, but she also possesses a sharp mind and displays a lot of critical thinking towards both Light and Dark Side archetypes. Contrary to what you'd expect from a Jedi (even a Fallen one), her affection for you is only affected by strategic acts of kindness (ones that improve other's lives in long term), but not by being merely nice and compassionate to everyone. If you don't actively corrupt her to The Dark Side, she eventually arrives at her own philosophy of the Force (not unlike Darth Revan's) that combines the best aspects of both Sides of the Force and is guided by reason.
Almost all of the good guys in The Order of the Stick fall under this trope, with the exception of Elan - who has his moments with his extreme Genre Savvy. Paladins even state outright (several times) that they're "Good, not dumb." Miko is an inversion; she is pretty smart, but her warped view of the world leads her to make increasingly bad judgement calls.
Arthur in Arthur, King of Time and Space. His enemies often assume that because he's nice, unassuming, and prepared to give the benefit of the doubt if possible, he can't be dangerous. Many of them are dead now, and the remaining ones still haven't learnt.
Girl Genius: Everyone thinks that just because Gilgamesh Wulfenbach never built a Death Ray and tries to be civilized and fair, they can push him around and act like he's nothing. When he's finally pushed over the edge, he shows the entire world that yes, he does know how to build a Death Ray, and yes, he's perfectly capable of kicking the crap out of Europa to protect his father and not-girlfriend.
When he does flip out and brings this up, he scares some very hard to scare people, while delivering an incredible beatdown to the oversized war criminal sent to retrieve him. And at the end:
Gil: Well, you know what? I can do crazy. I really can. And it looks like I'm going to have to. Agatha is in danger. This whole town is in danger. If I'm going to be able to help her at all, I'm going to have to give up all this "being reasonable" garbage and show you idiots what kind of madboy you're really dealing with! [Smashes Vole apparently through a wall, Beat, sudden wide eyes] ...oh. Oh, no. This must be how myfatherfeels - all the time!
In the Justice League episode "Flash and Substance," Orion asks why Central City would honor a buffoon like the Flash, "who makes bad jokes, who concerns with pitiful men like the Trickster." But the Flash is anything but dumb—he's able to handle the Trickster without throwing a single punch. In fact, he actually convinces the Trickster to happily turn himself in to the police.
He also defeated the Insufferable Genius Grood in one episode by outsmarting him, leading his teamate Green Lantern to remark "Well, maybe you aren't an idiot." (Probably being at least partially sarcastic.)
You can tell that even Batman is almost envious of his ability to quietly shut down a super-foe without violence, something he cannot imagine being able to do in Gotham... or anywhere else, for that matter. It does help that The Rogues (In the animations) are Punch Clock Villains rather than crazies Batman has to deal with. The Comics are another story:
Flash: "Do you think the Rogues here are simple? Do you think just because they aren't mentally screwed to the hilt that I have an easy time? Your guys are different, Bruce. They work on a completely cerebral level. They leave clues. They like to kill. My guys? They're organized."
In the Kung Fu Panda Legends Of Awesomeness episode, "Bosom Enemies," Po bends over backwards trying to let Taotie redeem himself, only to have him throw it away at being called an "assistant," and attack the panda and his friends. However, Taotie seems to have turned again and helps Po stop his machine and for a second it seems that Po has forgiven him. However, it turns out that even Po is not that naive and this treacherous villain is next shown in Chorh-Gom Prison.
Optimus Primal, quite possibly the intellectual equal of Magnificent Bastard Megatron, and more than once able to let the bad guys play right into his hands. Also a great guy in general, and a friend to all the Maximals under his command. Would rather not have to fight, but is very good at it.