In Death Note, L and Light both reveal themselves to have excellent hand-to-hand combat skills. Light is the definition of a perfect over-achiever, so we can assume that martial arts are just another one of his many extracurricular activities. The reveal is somewhat more surprising from L, who seems to spend every waking moment alone, crouched in front of a screen. Watari also suddenly reveals himself as a Battle Butler sharpshooter.
Dr. Reichwein of Monster used to work with the border police, but the two punks trying to beat him up in an alley didn't know that.
Mikoto Misaka of A Certain Magical Index turns out all of a sudden to speak both English and French in later stories. Perhaps justified in that she goes to a very prestigious and formal school, whose curriculum would likely include foreign language courses, but it comes up out of nowhere in the narrative.
In Getbackers, Van suddenly plays the violin in a perfect duet with well-known violinist Motoki, much to the surprise of everyone present especially Ginji who has been a job partner/friends with Van for years.
In the film Three Kings, one National Guardsman suddenly reveals himself as an airport baggage handler in civilian life when a need for detailed knowledge of suitcases arises.
In The Poseidon Adventure, Shelley Winters' character, while seemingly the least fit (and least useful) of the survivors, was able to swim a long distance underwater while carrying the end of a rope, because she was on the swim team in school. Sadly, she dies of a heart attack immediately afterwards.
In the film °Three Amigos!, Ned Nederlander reveals that he actually is a real quickdraw artist when challenged by a German former fan. The German assumed that Ned used trick photography, but Ned insists that it's all him. Subverted by Ned later when he reveals that he learned to fly the German's exact make and model of bi-plane for a film, but his stuntman actually did the flying. He still manages to fake it long enough to escape.
2012 loves to use this trope. For instance, Gordon Silverman is a plastic surgeon who is also an amateur pilot. He is used to help fly a plane when the group needed a pilot. Of course, a day's worth of flight lessons in a two-seater Cessna doesn't qualify you to fly the diversity of aircraft he pilots in the film. Hell, it barely qualifies you to fly a two-seater Cessna.
Star Trek: Nemesis has an extended sequence of Picard and his away team of Data and Worf speeding through the desert of an industrial-age planet to pick up the pieces of a Soong-type android that were picked up on sensors. According to Patrick Stewart, it was so he could do a bit of Cast Show Off due to his enthusiasm for dune racing in real life. While this makes sense for Patrick Stewart, Jean-Luc Picard was a man who upheld the Prime Directive at the risk of his own life over the course of his career, and yet this scene has him engage in a protracted chase scene with the some of the planet's inhabitants' military.
Enforced in The Matrix when characters have new skills downloaded directly into their brains, for example Neo being given fighting skills or Trinity learning how to fly a helicopter.
Alice in Resident Evil: Retribution suddenly knows American Sign Language so she can talk to her "daughter". Of course, given the character...
In Jack Vance's Lyonesse trilogy, Aillas never comes across as someone particularly interested or skilled in swordsmanship. In The Green Pearl, however, he encounters an infamous bandit leader from a very martial culture who considers himself virtually peerless with a blade in hand. Out of nowhere, Aillas hands him a Curb-Stomp Battle without breaking a sweat. A few chapters later, a bystander comments that he's a "demon with a sword."
Mk Venner, from Dan Abnett's Gaunt's Ghosts novel, really does know kung fu. Before joining the Imperial Guard he trained with a group of secretive 'woodland warriors' and also speaks fluent Old Gothic. Of course, you don't learn this until it saves the whole squad in His Last Command.
In Atlas Shrugged Dagny flies an airplane when she goes searching for John Galt. It is never mentioned why or how she knows how to fly.
Lampshaded in Redshirts, in that the Narrative will insert info into a character's head as the plot demands it.
In Witches Abroad, Granny shows amazing skill at the card game Cripple Mr. Onion, winning back the money and broom that Nanny lost to a group of gamblers. It turns out that she'd played daily with an old witch (who had only a vague idea of the difference between the present and future due to glitchy second sight) while keeping her company and picked up a few tricks.
The Dark Tower: Roland reveals a number of amazing abilities throughout the series, with no hint of possessing them earlier, including an encyclopedic knowledge of riddles, outstanding dancing skills and the ability to keep perfect time.
Honor Harrington does this a couple of times with armed combat abilities. (In contrast to her unarmed skills, which are set up from square one.) In particular, her excellent marksmanship shows up in Book 6. When asked how she was able to beat experienced fighters, she explains that she grew up using those skills in a region on Sphinx that wasn't too civilized, and actually considered joining the armed combat teams in the Navel Academy but went for unarmed combat instead. A bit later, she turns out to have a remarkable aptitude with specifically ancient firearms (i.e. real-life guns) because she was a member of the 40th century SCA.
Xander (once mentally turned into a soldier by a spell) knows the layout and lingo for the local military outpost. When these turned out to be useful, the writers Hand Waved them away... and Xander didn't even tell us about that until months after his implanted memories were gone. It does take about three years for the implanted memories to fade, which is a reasonable amount of time considering the spell that gave him those abilities only lasted all of several hours.
In the seventh season, the writers seemed so desperate to justify Dawn's very existence that she suddenly could translate old magical books from sumerian. It was slightly less justified than the same character demonstrating sword proficiency in the last episode of the sixth season.
Angel. Photographic Memory, Super Reflexes, ultra-sensitive hearing and sense of smell in the later seasons. When you re-watch the earlier seasons, you can't help but notice countless situations where, in retrospect, they inexplicably fail to help him. Angel mentioned that he can't control his photographic memory; it just "kicks in on instinct".
In Castle there there are several instances. At least Once per Episode Castle brings up some random piece of knowledge that his research or various hobbies have taught him. He can also speak Mandarin, which he attributed to a TV show he used to love.
Beckett can also slip into a Russian accent which she attributed to a semester she spent abroad.
In Charmed in "That Seventies Episode", Phoebe suddenly reveals the ability to pick locks. Lampshaded by Prue, who rhetorically asks, "Why am I not surprised that you know how to do this?"
Catherine, typically the classiest and snootiest character on NewsRadio, nonetheless knows a little three card monte from a summer spent hustling with an uncle.
Dave Nelson also has a surprising amount of skill in both knife throwing and tap dancing. He also just so happens to be a ventriloquist, speaks Spanish, is an expert at the arcade game Stargate [Defender], can sing a cappella, and can cross dress surprisingly well.
Diane on Cheers was an excellent bowler because she had taken bowling for her PE credits in college.
Quantum Leap's Dr Sam Beckett has seven degrees (most of them unidentified) and knows eleven languages. On the other hand, the Time Travel process leaves his memory swiss-cheesed, so he can forget as well as remember things as needed by the plot. Also, any skill he doesn't have can be taught to him by Al, who has been an astronaut, a boxer, a stage actor, a baseball pitcher, and even teaches Sam how to out-draw an old West gunslinger. In fairness, if you were looking for someone to be a holographic observer you'd probably want to get someone who is pretty handy, especially since they can't physically help. And Al is clearly old enough to have been all these things.
Al has also been married five times, and when information he gives Sam seems too arcane for even Al to have personally experienced, he often claims he learned it from one of his ex-wives.
There was an episode where Sam, in a life-threatening situation two switchblade-wielding kidnappers/rapists, was able to fend off his attackers WITH KUNG FU! After high kicking one of the scumbags, Sam was surprised to learn that he could do that, immediately after which Al informed him that he was skilled in several schools of martial arts.
Imagine how the people around him (who see Sam as their friend/family member/whatever) felt!
It's even in reality TV: In the Survivor All Star episodes, shortly after Richard Hatch gets voted off, we find out that Lex has a talent at fishing (which we never knew from Survivor Africa, because the only water Lex encountered there was at the bottom of a muddy hole).
In LOST, several characters have developed useful skills that have proven critical on the Island. Sun's knowledge of the medicinal qualities of herbs found on the island exceeds those of a normal home gardener, and Kate's "tracking" skills came out of nowhere (explained by a You Didn't Ask). However, this may be still explained by the mysteries of the island.
It seems like Sun's skill is less knowing what plants can do and more being able to figure out the name of a plant by looking at it — something that she could have picked up from books. It doesn't take a genius to know that eucalyptus is the active ingredient in Vicks Vapo Rub.
Shepherd Book of Firefly displayed an array of crime-related talents and knowledge that one wouldn't expect the average priest to have, hinting at a Mysterious Past; however, it was never made quite clear what this past was, beyond being former Alliance and his survival being very important to the authorities (except possibly non-canon Serenity book tie-in, where he reveals to Mal that he is a former Operative).
The Serenity RPG has characters buy their skills as they go, the justification being that we find some new facet of the character's backstory at that point.
Word of God has said that's canon now, as "Book" is actually the name of someone he killed.
On Friends, Chandler has hidden from Monica that he's an excellent ping-pong player, because he didn't want her to enter them in doubles tournaments. When she hurts her hand during a game, he turns out to be a not-so-hopeless replacement.
This was hinted several times early on, with Chandler mentioning playing racquet ball with his bosses (which included the strong implication he always let his bosses win), or Ross' parents. This was probably something written in, because of Matthew Perry's real-life brief career as a tennis player.
Chandler: I'll just play left-handed.
Ross: You mean you're not left-handed?
Sandra Bennet of Heroes can make fake IDs, a skill she used to sneak into Def Leppard concerts when she was younger.
In the Bones episode "The Woman In The Sand," the normally clipped and clinical Brennan unexpectedly busts out a scarily convincing alternate persona to fool some lowlifes, complete with Jersey-girl accent. When Booth later asks her "what got into you," she says, "Itís from when I used to watch old movies with my dad. He really liked Clara Bow."
"Clara Bow was a silent film star, Bones."
"Yeah, but I guess that's how I always imagined she sounded."
Possible Genius Bonus; Clara Bow was a Brooklyn native and had a notoriously thick accent.
Considering how Brennan's father is a human chameleon who's successfully adopted multiple false identities for years, it'd be surprising if his daughter couldn't fake one for at least a few minutes.
In The A-Team episode "The Maltese Cow," Face and Murdock find a message written on a mirror in Chinese. Murdock proceeds to read it out loud, and when Face gives him a weird look, he explains:
Murdock: One afternoon, I got a gonzo headache, and before it was over, I could read and write Chinese. And that was a bad afternoon, let me tell you.
Trick's Ueda Jiro, virgin physicist professor, took a correspondence course in karate that somehow turned him into a kung-fu machine.
In Taxi, Jim Ignatowski is brought to a fancy party by Elaine who is hoping to impress someone but needs a date to attend the party. Jim proceeds to humiliate Elaine by acting like the '60s burn-out that he is, only to save the situation by sitting down at the piano and playing brilliantly. The other guests assume that Jim was just having a bit of fun, and so Elaine succeeds in her goal. Jim's befuddled reaction to his own playing: "I must have taken.. music lessons..."
In the Made-for-TV Movie/Pilot MoveTag Team two pro wrestlers are drummed out of the business for refusing to take a dive and become cops. At the police academy one (played by Jesse Ventura) shows remarkable marksmanship. "Where did you learn that?" "Navy SEALs."
Psych is a borderline example since episodes generally start with a flashback to Shawn learning a skill that will prove relevant to the episode. It still counts, though, since we never hear about any of these skills until the episode in which they become useful.
Chakotay from Star Trek: Voyager is infamous for this. As sfdebris puts it, "because Chakotay's always been interested in... (sound of rolling dice) ...anthropology!"
In the serial "The Gunfighters", the Doctor's cover identity for himself, Steven and Dodo is that they are all travelling performers. He quickly fibs that Steven is a singer and Dodo is a pianist, both of which they yell at the Doctor for as they claim they can barely do those things. When they're later forced to perform a sophisticated ragtime song they have never heard before, with no rehearsal, from sheet music, they are surprisingly good - Dodo even enjoys her piano playing so much that she gets jealous when the gang forces Steven to play piano, at which he is also surprisingly good. Both of them express surprise at how good they all are afterwards.
In the same serial, the Doctor, who normally Doesn't Like Guns, suddenly becomes able to do Gun Twirling when showing off to Wyatt Earp (who suggests that doing it is a bad idea).
The Doctor has this as a character trait - different incarnations of himself suddenly display 'new' skills he'd apparently known forever, or forget old ones, helping to differentiate new incarnations. Obvious examples are the Second Doctor's social accuity, the Third Doctor's mastery of Venusian aikido, the Fourth Doctor's rather stronger Psychic Powers than the others, and so on. In the Virgin New Adventures books, the Seventh Doctor temporarily reverts his personality (though not his body) to that of the Third Doctor - once to take advantage of Three's martial arts and once to take advantage of his different scientific knowledge.
The Expanded Universe takes some pleasure in giving previous Doctors powers only shown by later ones. For instance, the Time Trips novella "The Death Pit" shows the Fourth Doctor using psychic paper to blag his way into a spa, a gadget introduced by the Ninth Doctor.
In Yu Gi Oh East Academy: Duel Spirit powers pop up left and right, from Gol'gar's mind-reading and Machine King's ability to hack anything to Denero and Meteor's ability to merge permanently. Justified since this happens early on in the series when such things are normally introduced.
It's not uncommon for characters using kung fu in Feng Shui to claim that a particular ability their player bought with XP was something they knew how to do all along. As the book explains, "Action heroes pull this one all the time."
A "cinematic" Advantage proposed by S. John Ross for GURPS is Up To The Challenge, which says that, within limits, a cinematic character can Suddenly Have Always Had Skills, as long as he spends the Character Points for them later.
"On the fly" character creation in Fate-based games like Spirit of the Century has shades of this — rather than detailing their characters fully in advance, players using this method start with only a minimal outline (an aspect or two, their peak skill and such) and simply fill in the blanks as they go along. Eventually there will be nothing left to fill in, of course, and the character will operate under the normal advancement rules from that point on, but until then this trope applies in full.
In Act V, Scene II, Hamlet announces that he has "been in continual practise" at fencing since Laertes went to France. Kenneth Branagh's film version actually has Hamlet practicing continually.
The computer game Planescape: Torment gives us The Nameless One, an amnesiac immortal (or is it immortal amnesiac?) who, rather than learning skills from people that he meets, instead remembers whatever skill it was that he forgot, that, occasionally, he taught the teacher ages ago. It goes a step further by having you relearn skills by re-attaching severed body parts that you had already grown back, which involves re-severing them. And one of them is your eye.
Gordon Freeman: the 27-year-old theoretical physicist who just happens to be a crack shot with all types of human and alien firearms, in addition to being able to expertly wield a crowbar as a weapon. At least the Hazard Course involves firearms training to help explain it because according to Word of God, the only weapon Gordon ever held in his hand prior to joining Black Mesa was a butane-powered tennis ball cannon he built as a kid.
Metal Gear Solid 3: Snake Eater introduced CQC fighting techniques to the series. They were brought back for Metal Gear Solid 4: Guns of the Patriots, which resulted in some oddities since 3 is a prequel set at least 30 years before the first game. So, it was retconned that Solid Snake always knew CQC because Big Boss taught it to him. In one Codec, Otacon asks why Snake never used it before, and he claims it's because of its association with who became one of his worst enemies. His use of it now is handwaved with a side-order of Leaning on the Fourth Wall - Big Boss' pre-Outer Heaven exploits had been declassified between the events of 2 and 4, meaning the war economy's modern PMC soldiers all know what Snake describes as a "pale imitation" of CQC; when they try to use it on him, he instinctively responds by showing them how it's really done.
At one point in the bonus chapter of Stranded Dreamscapes: The Prisoner the main character had to weld an unattached hook to a pole in order to pull down a fire escape, prompting her niece to remark "You know how to weld, Aunt Helen?" Precisely why this was stranger to her than a talking teddy bear sidekick was left unexplained.
George of Umineko no Naku Koro ni reveals he knows a multitude of martial arts while fighting Gaap in the fourth story arc. Granted, it was known as early as the start of the first arc that his mother Eva was a skilled martial artist, and that she taught George many, many things to become the talented and successful man he is. But because it wasn't known that martial arts was one of those "many things" until later, it still counts.
In Harkovast, Chen-Chen at first seems pretty helpless, but is suddenly revealed to be a master of the sliding mountain style, which allows her to kill armed opponents with her bare fists.
In The Order of the Stick, Tarquin's skill for communicating in Drow sign language is only mentioned once. Conveniently, it's brought up right when he needs to give orders to a Drow who was recently deafened by a spell.
Played with in one Global Guardians story: a villain tries to hold inoffensive precog heroine Second Sight hostage in order to escape. Second Sight, whose powers all revolved around her clairvoyant ability to see the future, took the villain apart with previously unseen Kung Fu skills. It turned out the skills had been there since the creation of the character. They'd just never been needed before.
Hey Arnold!!, "Road Trip": Helga's mom can ride bulls and was once a champion rodeo girl in her youth.
In one episode of Kim Possible, Dr. Drakken hypnotizes all the senior citizens in Florida, including Kim's Nana, who it turns out has had quite an interesting life and picked up an assortment of skills, including piloting, race-car driving, and of course martial arts. Drakken somewhat lampshades the situation that Kim knew little about her grandmother.
Winx Club had fashion-obsessed Stella solve a puzzle in one episode by remembering a minor detail from a field trip they took for magical history class. (It should be noted that this is a 4Kids dub change: in the original, it's her love of fashion that helps her solve the puzzle, although with this method she essentially stumbles on the solution.)
The Boondocks. Who knew Uncle Ruckus "had mastered the ancient and deadly art of the nunchaku".
In the Justice League episode "Hereafter", Superman awakens on a wasteland planet with a red sun, robbing him of his powers, with only a city street's worth of objects to assist him. As he attempts to find a way off, the human-level Kal-El displays shocking aptitude in blacksmithing, sword fighting, auto repair and even dog sledding as he traverses the blasted landscape. However, he IS a farm boy. He probably had to learn many repair and maintenance skills growing up and kept learning new things. The reason of the shock is because of how many view him as someone who only relies on brute strength.
In Futurama, it is revealed that Dr. Zoidberg's doctorate is in art history when the main characters need to analyze a Da Vinci painting.
Pam in Archer gets some serious re-characterization over the first two seasons. She starts out as a rather pathetic, overweight office gossip and Abhorrent Admirer. In one episode, however, it's revealed that she's a champion bare-knuckle boxer implied to have killed thirteen men in the ring. In another episode, she's revealed to be an amateur street racer who regularly takes on the Yakuza. In yet another episode, it's revealed that she's a sexual dynamo who amazes even the ladykilling Archer.
Cheryl turns from an insecure, unhinged secretary to a full blown insane sex maniac in the space of about 4 episodes.
In the season 5 premiere, Cyril out of the blue reveals that he is a former defense attorney. The show also parodies it, as Cyril laments the fact that he has had several "long talks" about this with Lana (off-screen), but she apparently doesn't remember them. The writer flat out admitted that was made up to create a reason for keeping him around during the ISIS crew's new career as drug dealers.
On The Cleveland Show, Cleveland Jr. begins to serenade his betrothed, Cecilia, and demonstrates the previously unmentioned dual skills of playing the guitar and fluency in Spanish. Lampshaded by Cleveland.
In one Tiny Toon Adventures episode, Buster and Babs rescue a baby beluga whale — and can communicate with it easily thanks to Babs, who in her own words "just happen(s) to be fluent in Whale".
When Uwe Boll challenged his many critics to a boxing match, most people thought it would be in good fun. It turns out that Boll was a semi-professional boxer before taking up direction. He beat the ever-loving snot out of several untrained critics who went into the ring with him. It should be noted, however, that Boll openly cherry picked his opponents and openly ducked Seanbaby, who knows Muay Thai and is much larger.
While filming a scene where a character is stabbed (repeatedly) in the back, Christopher Lee explained to Peter Jackson that when that happens, the victim doesn't scream (one's lungs being punctured might have something to do with it). When asked how he knew, he explained that during WWII, he was in special operations. The story is told in The Lord of the Rings's extras.
This crops up a lot in countries where compulsive military conscription is the law or was until recently. For example the nice middle aged gentleman might have once been Spetsnaz, the fellow walking down the street might have been a medical corpsman or your disgruntled worker might have set claymore mines as a combat engineer...
Happened twice on the set of The Great Escape. Donald Pleasance had been an actual POW in a Luftwaffe camp before the movie, and James Garner was the scrounger for his unit in the Korean War.
Also when filming The Dirty Dozen: Lee Marvin proceeded to disassemble and assemble his gun without the gun master help - Marvin had served as a Marine in the Pacific War.
One interviewer asked Mayim Bialik if it was annoying when fans assumed, because she plays a neurobiologist on The Big Bang Theory, she was really that smart and asked her if she could do calculus. She replied that she actually is a neurobiologist and is very good at calculus.