Samantha "Sam" Sparks in Cloudy with a Chance of Meatballs was secretly a nerd in her school days but hides her brains behind the facade of the pretty, ditzy weathergirl for fear of being stigmatised. It adds another layer to the character that she is voiced by Anna Faris who is more well known for playing genuinely ditzy characters.
Big Hero 6: At the beginning of the movie, Hiro goes to a back-alley robot fighting competition with a pathetic-looking robot, and shyly asking if he can fight too. After getting beaten in a couple of hits he asks if he can bet more money for a second chance. When the second fight starts he drops the shy attitude and shows his robot's true talents by utterly destroying the rival's robot.
Iago from Aladdin pretends to be a normal parrot in front of everyone but Jafar. At least until the climax.
Films — Live-Action
Bill Cosby: Himself
Bill: (on being incompetent fathers who use incompetence to get out of chores) You see, we are dumb, but we're not so dumb.
Captain Jack Sparrow, Pirates of the Caribbean. You might think he's quite a harmless fellow when you lock him in chains, but if you start a 10 minute long conversation with him, he'll probably talk you into opening his chains, steal your pistol and threaten you with it, make a break for it and steal the ship you should be guarding before you can even realize what the hell just happened. And when you reach out for your pocket to get the whistle and call the guards you'll notice that your wallet is also missing...the quotes below give great examples:
Norrington: No additional shot nor powder, a compass that doesn't point north...(looks at Jack's sword) And I half expected it to be made of wood. You are without doubt the worst pirate I've ever heard of.
Captain Jack Sparrow: But you have heard of me.
(Shortly after, when their ship is stolen by two people, including Jack)
Lt. Groves: That's got to be the best pirate I've ever seen."
James Kirk in the new Star Trek film practically turns this into an art form, frequently acting like a womanizing idiot or playing the fool throughout parts of the film. However, it quickly becomes clear that he's not nearly as stupid as he leads people to believe, effectively beating the supposedly unbeatable Kobayashi Maru through rather ingenious means and then stopping Nero's rampage of revenge against the Federation. Prior to joining Starfleet, it's even stated by Pike that Jim's the only "genius-level repeat offender in the Midwest."
If you watch closely, you will notice that the "brainless" Scarecrow is the one who has all the ideas, comes up with the plan to sneak into the witch's castle, and even (at the climax) manages to think quickly enough to use the Tin Man's ax to drop a chandelier on the witch's soldiers. This is even more pronounced in the original book, where he comes up with clever solutions to nearly every obstacle and monster that the Witch of the West and Oz itself throws at them. In both versions, the Scarecrow's dumb act has even fooled himself. He associates intelligence solely with being a "great brain" or "deep thinker". Since he's not one of those by any means, he fails to recognize his planning, quick thinking, and resourcefulness are also signs of intelligence.
In the musical version of Wicked, it is implied that the Scarecrow, actually a transformed Winkie prince, knew he was the most intelligent of the group, but faked stupidity so that he could join up with Dorothy and return to Elphaba.
Miss Gulch: I'm all the lame for the bite on my leg.
Uncle Henry: You mean she [Dorothy] bit you?
Miss Gulch: No, her dog.
Uncle Henry: Oh, she bit her dog! Whacks the gate closed onto Miss Gulch.
Miss Gulch: No.
Zatoichi, in the series of movies of the same name, posed as a harmless blind masseur (he really was blind) until it came time for either intimidation or the mass slaughter of the Evil Minions.
Blind Fury, an American version of Zatoichi set in 1980s America, has the main character acting like a foolish and unassuming drifter. When set upon by a pack of thugs, he pretends to accidentally take them all out with a Plank Gag and other seemingly innocent movements.
In The Pink Panther (2006), it is revealed that Inspector Clouseau could speak Chinese all along and figured out who the killer was when the Chinese woman named "Yu" was brought in for questioning. His rant about actually knowing Chinese turned out to be true.
Budd from Kill Bill is depicted to be a drunken redneck who works as a bouncer for a titty bar. Nonetheless he has shown a philosophical side and is the only Viper to get an advantage on Beatrix Kiddo, by faking unawareness that she's hiding around his trailer and blasting her with rock salt when she busts through his door. In fact, Budd is the only of the vipers not to be killed by The Bride (well, Elle is not actually shown dead, but is at least very thoroughly screwed).
Silent Bob, from Kevin Smith's The View Askewniverse appears to be little more then Jay's silent companion, only less exuberant and dumber. It turns out that he's quite knowledgeable. Silent Bob may seem smarter than Jay because his friend is very loud. In Mallrats, Silent Bob apparently won his eighth grade science fair by turning his mom's vibrator into a CD player with "chicken wire and shit"
Yoda in The Empire Strikes Back is introduced this way, pretending to be an irritating little creature who steals food and squabbles with R2 before finally revealing himself to be the ancient and powerful Jedi master. It's all a Secret Test of Luke's patience.
Jackie Chan tends to play these kinds of characters, particularly in Rush Hour, when he allows Chris Tucker's character, Carter, to believe he doesn't speak English. Carter gets him back, though, when he reveals that he can speak Chinese just fine. The Screwups Reel makes it quite clear, however, that Tucker himself can't, and since he doesn't speak Chinese in the second movie either, it's possible that Carter only knows the basics of the language or learned just enough for the prank.
In both the 1940 and 1920 versions of The Mark of Zorro, Diego de la Vega plays the featherbrained fop to lull the corrupt Governor Quintero, while, as the masked swashbuckler Zorro, trying to frighten Quintero out of the country. And the 1974 made for TV movie with the same title. Frank Langella's portrayal of foppish Diego de la Vega is the greatest bit of the film.
The janitor in the horror film Disturbing Behavior pretends to be mentally handicapped because it causes people around him to drop their guard and become "interesting."
In The Usual Suspects, Verbal Kint, pretending to be a weak-willed and crippled sap who was taken advantage of by Dean Keaton, rather than the diabolical crimelord he is.
In Superman III, villain Ross Webster's assistant and girlfriend Lorelei acts the part of the Dumb Blonde but is secretly highly intelligent (when alone she reads Immanuel Kant's Critique of Pure Reason and disputes one of Kant's arguments). As a result she's able to outwit Ross and his sister.
In Horse Feathers, Connie plays up her football ignorance to try to get Professor Wagstaff to share his secret signals. She overdoes her childlike ditziness, so either he sees right through the ruse or he thinks she needs to snap out of it.
Subverted in The Court Jester: some of the villains, believing the title character is either an assassin they hired or a Robin Hood-esque resistance leader, believe he's doing it. In fact, he's actually a carnival performer who really is that twitchy and bumbling.
Dewey: "How do you know that my dimwitted inexperience isn't merely a subtle form of manipulation, used to lower people's expectations, thereby enhancing my ability to effectively maneuver within any given situation?"
(a brief pause, then Gale starts laughing)
In Mr. Baseball, Tom Selleck plays an American baseball player who signs up with a Japanese team. The team's manager appears not to know English through most of the film, causing grief for Selleck's character when he finally finds out.
True Lies does this beautifully several times, though it borders on ridiculous when Harry calls the obvious nuclear warhead an espresso machine...of course at that point it's clear he was being sarcastic to annoy the terrorists.
Summer of '42 has its underage protagonist employ some of this to obtain some condoms from a pharmacist. When asked what he wants them for, he says they're actually for his (nonexistent) older brother and that he assumes they're for filling with water and dropping on people from a roof.
In Dumb and Dumber, the kidnappers only think Harry and Lloyd are doing this.
In the sequel, Harry actually plays it straight, admitting he already figured out that Lloyd was faking his depression before Lloyd admitted it himself, pulling off a prank to make Lloyd think he needed a kidney.
In Maverick, Bret Maverick pulls this off effectively in an early scene where he invites himself into a poker game, saying, "I promise that I'll do nothing but lose for at least an hour." For the first hour of so he indeed loses every hand. From the second hour of the game on, Maverick winds up cleaning out the rest of the table. When one fellow gambler accuses him of cheating, Maverick explains, "What do you think I was doing for the first hour? I was learning your tells." This sets the tone for the rest of the movie, in which Maverick appears to be bumbling his way through the West, but in reality is as shrewd and sly as anyone else in the movie.
Gordon: You don't watch a whole lot of news, do you Mr. Wayne?
The Hallelujah Trail: Walks Stooped Over, the Sioux chief who does all of their negotiating in badly translated sign language, is revealed at the end as speaking perfectly good English.
Both Mr. Green and Colonel Mustard both embody this throughout most of the film Clue. Although, depending on which ending you get, it's completely genuine for Green.
In The Avengers (2012), Natasha Romanoff uses a variation of this combined with a Wounded Gazelle Gambit as an interrogation technique. She lets the interrogat-ee think that they've outwitted her and plays the part of the helpless prisoner, then waits for them to shoot their big mouth off while they're gloating about how she failed to live up to her reputation. Then she breaks out and kicks the shit out of them. This scene is just foreshadowing for when she pulls a similar trick on Loki.
David "Mo" Rutherford, in The Stuff. He portrays himself as a quite inept and dimwitted lowlife, introducing himself in a particularly obnoxious manner. The trope quite soon lampshaded when one character, impressed with Mo's ingenuity in placing a small microphone into the pockets of everyone in present at the meeting on the night before, comments "you're not as dumb as you appear to be". To which he responds "Nobody is as dumb as I appear to be".
Mr. Shhh (played by Steve Buscemi) in Things to Do in Denver When You're Dead. He's introduced with narration showing up in a slightly disheveled suit and slumped shoulders. He proceeds to kill a couple of muggers without breaking a sweat.
In My Fellow Americans, former Presidents Kramer and Douglas run for their lives, trying to discover the criminal genius who framed them for a bribery scandal. Turns out it was the supposed fool of a Vice President, Ted Matthews, who arranged to remove both the former Presidents and his own boss with a single scandal.
Funny thing is everybody thinks I'm this big idiot, and its all a big facade. (While mispronouncing facade as fah-sid)
Vanko shows he's both fluent and eloquent in his early face-to-face confrontation with Tony Stark, but speaks to Hammer in broken, barely intelligible English just to dick with the guy. Later on he acts only barely competent at engineering and technology, convincing Hammer that the best he can do with the Hammer suits is to make drones and then later on that the best he can make the drones do is "salute." Hammer naturally underestimates him as a result.
As a Bilingual Bonus, he adds a definite "y" to the word "salute" to make it sound like "make salyut". While someone might assume that this is just a harmless Russian mispronunciation, the Russian word "salyut" (Салют) is the English word "fireworks". Which is what happens next.
Tony pulls this himself - even though everyone knows how smart he is (largely because his Awesome Ego won't let him keep his mouth shut about it), he plays at being much less intelligent at human interactions than he really is, and more of a dissipated playboy than he really is. This is particularly noticeable in the fight scene in Iron Man 2 between him and Rhodes in the Mk II. While before he was dancing as if drunk and shooting liquor bottles with his repulsors, during the fight he's just as quick as Rhodes and gives easily as good as he gets.
Big time in Now You See Me. Rhodes is always one step behind the Four Horseman and is always outwitted by them. He's actually the Fifth Horsemen, deliberately pretending to fall for all their tricks to make sure the authorities are always one step behind the Horsemen.
In Django Unchained, Stephen plays the role of a submissive house slave in public. In private however, he's actually smarter than his master and serves as Candie's personal adviser. It is later implied Stephen makes most of the decisions on the plantation, by convincing others his ideas are their ideas.
Mean Girls: Despite being a math genius, Cady pretends to be bad at maths to get Aaron to tutor so she can spend time with him. Karen might be possibly be this as well.
Miss Congeniality: Most of the girls come across as the stereotypes Gracie associates with pageants, but for the most part this is because the girls are all very well-trained in saying exactly the right things to get them the points needed to win, even if makes them seem brainless. Cheryl, who spends most of the film appearing to be a sweet and gentle Dumb Blonde, turns out to be a nuclear physicist.
Fracture (2007): As part of his scheme, Ted Crawford, who's being tried for attempted murder, initially presents himself as a layman unacquainted with courtroom procedures but who decided to represent himself by exercising his basic rights, presumably out of hubris. When he later pushes for an acquittal based on lack of admissible evidence by the prosecution, he reveals that he has quite a bit of legal expertise, which the annoyed judge quickly notices. You can especially see it when he uses the legal phrase "motion for judgment of acquittal", not having demonstrated any familiarity with them earlier.
The Film The Idiots is about a bunch of middle class teenagers and 20-somethings that pretend to be mental retarded in order to fuck with people. And of course when the leader of The Idiots actually encounters someone mentally retarded he flips completely out on them. Needless to say the movie does not end too well.
Although Nathan is obviously a genius as an inventor and can talk technical if he wants to, he tends to play up his flaws and act easier to exploit than he really is. He might have affected or at least exaggerated his drinking problem and hipster/bro personality so that Caleb would be suckered into trying to trick him.
In The Captain Hates the Sea, Schulte the PI is following Danny Crockett on the cruise ship, trying to get the $250,000 in bonds that Danny has stolen. Danny's Outlaw Couple partner Janet, aka "Michigan Red" and posing here as an innocent librarian, manipulates Schulte into falling in love with her in order to distract him from the bonds. Schulte appears to be falling for their scheme, until he's shown holding Janet's rap sheet, revealing that he knows everything.
This is Billy's act in White Men Can't Jump; he pretends to be a goofy white guy so that when he plays basketball for money, no one will realize how good he actually is.
Harry Deane, of Gambit, seems intelligent, but horribly naive and prone to screwing up everything. In actuality, he's the mastermind of a greater con than what he claims to be perpetrating.
Dawn of the Planet of the Apes: Koba pretends to still be a simple-minded chimp when cornered by a couple of humans with guns, so that they'll let him go, and does it again later so that he can get close enough to grab one of their guns and kill them with it.