Mr. Spock, and the Vulcan species, from Star Trek. What could be more non-threatening than a science officer (geek) with no emotion or ego? Well, screw with his ship or his captain and you'll find out pretty quick he'll neck pinch you into submission. You may also find out that Vulcans are, on average, three times as strong as humans. And if you really provoke him he willshoot the damn dog. Just to prove the point. And God help you if you say anything bad about his mother. He says at one time that the Vulcans were once barbarians who nearly killed one another off before adopting the teachings of Surak; it is strongly implied that the Romulans are descendants of Vulcans who would not or could not embrace Surak's philosophy.
Commander Data, as an android, has the mental processing speed of a computer as well as super strength and resilience. "I assume your handprint will open this door whether you are conscious or not."
Captain Picard is a reclusive classical scholar most of the time and doing things like pulling off political Batman Gambits against a whole empire, assuming the role of a hardened criminal to infiltrate a gang of mercenaries, and single-handedly defeating a group of terrorists the rest of the time. And ever since the last few scenes of Season Three, he has had Borg strength, too. The movies eventually take things a bit too far in the physical combat direction, but there's a good reason why he and Data relate so well to each other. Picard fought and killed two Klingons sent to murder him. He's also taken down more Borg drones in single combat than any other character, and he's endured torture multiple times. Oh yeah, a knife to the heart and (years later) a phaser bolt to the same spot were not enough to kill him. That's badass.
Montgomery Scott. One of the best engineers of his day, and a fierce barroom brawler when he's pissed off.
To a Klingon warrior that has just insulted his beloved Enterprise: Laddie, d'ya not think you should re-phrase that?
Deep Space Nine gives us Julian Bashir, an unassuming and very geeky medical officer who is revealed to have been genetically altered for enhanced physical and mental abilities, meaning he could have gone toe to to with Khan Noonien Singh had the opportunity presented itself.
And the women of Star Trek: T'Pol (standard Vulcan), Jadzia Dax (trained as a Klingon warrior), Kathryn Janeway (started out as a science officer and is the most trigger-happy captain except Kirk), B'Elanna Torres (half-Klingon genius engineer with issues) and Seven of Nine (Borg strength and intelligence in one pretty package).
Giles: Normally, he exemplifies the stereotypes you'd expect from a British librarian. He has a very soft spot for his books, but when the situation calls for it, he's willing to kick a little ass and show why he used to go by the nickname "Ripper." He once pulled a crossbow bolt out of his own back and stabbed a vampire with it and also makes a one-man assault on the factory after Angelus kills Jenny Calendar.
Willow is something of a geek, but sure can be dangerous. She took down Glory for a time, and she almost ended the world.
Fred probably qualifies. Although it isn't shown often, her engineering capabilities have at least once resulted in an insanely awesome guillotining machine.
Wesley also fits this trope once he was Rescued from the Scrappy Heap. While he was on Buffy and in early Angel he was for lack of a better word, a by-the-book, private-education pansy (although to be fair, it was Watcher education, so he was learning how to be Badass). After being tricked into stealing Connor and being ostracised by the rest of Angel Investigations? He became the epitome of good old Buffyverse badassery.
A very dark variation of this can be found in the title character of Dexter. Dexter is a forensic blood spatter analyst and often called a "lab nerd" by the more macho police officers. Despite this, he can kill anyone. He's also a surprisingly beefy specimen under that shirt, which is more obvious while wearing his form-fitting murder clothes. He's bested Doakes, an ex-Special Forces member and ultra-badass cop, twice in hand-to-hand combat, despite being shot in the leg right before round two. He also killed The Skinner, who was the leader of a Nicaraguan interrogation unit, with his bare hands. He did so one-handed, because he crushed his own hand to escape his bindings. Most recently, he has taken down one of the most skilled cops in Miami, herself a murderer, in close combat.
Gil Grissom from CSI: Crime Scene Investigation repeatedly emphasizes that he's a scientist, not a cop. It just so happens he's also an excellent shot with a handgun, on the few occasions it's come up.
Daniel Jackson from Stargate SG-1. This, however, was the end result of long, patient Character Development: just compare the innocent cutie from Stargate and "Children of the Gods" to the action man in seasons 9-10, and every relative degree of badassery in between in the other seasons.
An even truer example is Colonel Samantha Carter. Jack O'Neill said that her brain was a national treasure. That doesn't stop her from kickin' serious ass, alien or otherwise.
Rodney McKay from Stargate Atlantis also tends to fill this trope on a rare occasion or three per season. A very rare occasion, admittedly. Such as the time he was digging a rock out of his boot and was attacked by a Wraith. Rather than put his unbooted foot on the dirty ground, he emptied his magazine into the Wraith while hopping on one foot, killing it.
The Doctor, from Doctor Who. He started off as the feeble old scientist who had to have his younger and more physically-able companions do the legwork. When the plot required it, however, he became a master swordsman, or a blackbelt in Venusian Aikido, or even an expert in Good Old Fisticuffs. In fact, the Doctor is so much of a badass that he is feared by malevolent beings across the universe and throughout time. Most of his adventures were not exaggerated and his reputation as "the Oncoming Storm" is well-deserved.
Even as the 'feeble old scientist' it was often implied that he was faking a lot of the feebleness. "The Reign of Terror", "The Romans" and "The Time Meddler" show him winning physical fights with young assailants, although in at least two of those he did have to sneak up on his opponent first. In the second episode of "An Unearthly Child/10,000 BC" he tries to bash someone's brains out with a rock.
"The Family of Blood" spotlit just this with the final voiceover.
In "Forest of the Dead" the Doctor faces a microscopic swarm which can strip people to bare bones in a matter of seconds. His response? He tells them to look him up (they're in a library the size of a planet at the time). They do and immediately back down.
Similarly, in "The Eleventh Hour", The Doctor takes the Atraxi to task for endangering Earth and ensures that they will never repeat this transgression by informing them of exactly who he is and of what he is capable.
The Doctor: Hello. I'm The Doctor. Basically... run.
Currently, River Song may qualify. She's evidently a professor, and later, or earlier, a doctor, but is...pretty scary for an academic.
In "The Big Bang" she pulls the aforementioned "Look me up" trick on a Dalek which assumed that as an associate of the Doctor she would show it mercy. It soon learned this assumption to be entirely incorrect. And begged for mercy.
Martha Jones, too. She's a medical student...who ends up fighting aliens, and, on one memorable occasion, trekking around the entire planet and outsmarting the man who had total control of it via scary childlike deathbots and telepathic satellites. She was noted as the only person to escape Japan when it burned. And when her adventures with the Doctor were done? She joined UNIT, and after that became a freelance alien crime fighter.
Ian Chesterton and Barbara Wright. They have survived three run-ins with the Daleks, and it is heavily implied that they have survived a fourth with tougher Daleks.
Sam Beckett from Quantum Leap. A holder of multiple doctorates, speaks multiple languages, and happens to be a black belt in several disciplines.
Constable Benton Fraser on Due South uses his smarts to solve crimes and can handle himself very well in a fight.
There's Hotch, former coin collector and self-confessed nerd, whose specialty is Awesomeness by Analysis and sniper-standard crack shooting.
Rossi the author, interrogation specialist and video-game player.
Prentiss and Morgan, who both love Vonnegut. Morgan is the go-to agent for kicking down doors and hand-to-hand combat, and Prentiss once brought down an international arms dealer and his organization practically single-handedly.
Reid with his three PhDs, extreme amount of general (and pop-cultural) knowledge, who is also a damn' good shot when needed and can keep his head under any circumstances including slipping efficient little coded messages about his whereabouts into videos that a killer who has abducted him is sending to his fellow agents, WHILE being actively tortured and hepped up on dilaudid to boot, without even using his hands.
JJ, soccer player, butterfly collector and communications specialist who can take down a psycho killer through a plate-glass door in a perfect headshot.
Garcia, who's the Oracle of Quantico and goddess of things quirky and nerdy, and a vicious hacker when she needs to be.
Gideon the birdwatcher once baited a man about to shoot him in the head until he turned into a weeping, stammering mess.
Only Elle, Todd and Seaver don't fit the trope, and Todd and Seaver really wasn't really around for long enough to even show potential.
Similar to Dr. Reid above, in NUMB3RS, Dr. Charles Eppes gets talked into learning the combat skills of an FBI agent. As expected for a bookish sort like Charlie, he is terrible in most of the trials, especially in his pursuit driving lessons where he scares his instructor by his bad driving. This seems to include when Charlie tested for firearm proficiency when he seems to be shooting too slowly compared to the others. However, when Charlie's shooting target is brought back for examination, it has a big hole where most of the bullets hit dead center. Charlie explains how he got the highest shooting score by saying he followed the advice of the famous gunfighter, Wyatt Earp, "Speed is fine, but accuracy is final."
Noah "HRG" Bennet. At the start of season two, his boss at Copy Kingdom berates him and sneers at him for failing to respect the art of photocopying papers. A short session with Mr. Horn-Rimmed Glasses in the backroom, though, ends with two broken fingers and a never-to-be-repressed terror of his new employee. He dosn't have any powers, and still maganges to match everyone else by knowing how they work. And then, in a two-part episode, everyone loses their powers. And Sylar makes him mad
Sylar. One of the first things that the audience learns about him before he was revealed was that his apartment was covered top to bottom with books. When he's trapped inside an empty dreamworld in his own mind, any visible space shown on screen was covered with images of books and clocks. When Peter gets stuck inside Sylar's head, Sylar heckles him with a comic book and in return, he humors Sylar with a copy of The Pillars of the Earth.
River Tam is an unmatched genius of all sorts, but is unfortunately a complete mental wreck, on top of being a tiny, unimposing teenage girl. When confronted with danger, her typical response is of the crying, fetal-curling variety until she unlocks the ingrained Super Soldier training that came with her insanity. Legendary ass-kicking ensues.
Her brother Simon is a well-mannered and highly educated medic who detests violence and looks a complete sissy. That is, until someone threatens his dear sister.
Vampire Stefan. He is highly intelligent, scholarly and academic....and he can also kick ass.
Alaric. He is knowledgable and well-read. Not to mention that he is also a vampire hunter.
Hit man Brother Mouzone from The Wire. Inspires fear and respect in the entire Baltimore drug organization, with good reason, despite his small stature, bow tie and glasses, devotion to Harper's magazine, and frequent use of big words and carefully crafted sentences.
By the end of the series, one of the only people even half as scary as Aeryn Sun is her lover, former Smart Guy and now Badass Bookworm John Crichton. He started out pretty helpless, but trained by her and with his level of sanity consistently gently curving down into a plummet, he became the kind of guy who would threaten to suicide bomb with a nuke.
Another good example would be Scorpius. Originally introduced as an Omnidisciplinary Scientist and Torture Technician, subsequent episodes revealed that he was strong enough to throw Captain Crais across his office like a rag doll and wear armor that shrugged off pulse pistol shots. Doubly impressive considering the number of health problems Scorpius suffers from.
The series even parodied the trope in an episode of Dino Thunder where Lovable Jock Conner McKnight temporally became a Badass Bookworm thanks to a meteorite which changed the three Rangers' personalities (Cute Bruiser Kira became a dainty girly girl and the video game nerd, Ethan, became a Jerk Jock).
Kendrix Morgan from Power Rangers Lost Galaxy would probably count if not for the fact that it's safe to assume every officer on that space colony was given mandatory fight training.
MacGyver. Don't let his mullet and laid-back Minnesota drawl fool you: underneath that feathered-blond hairdo and behind all his folksy wisecracks lurks one of the most agile minds of any TV hero, capable of turning almost any collection of mundane objects into something amazing. He was so good at this that his name has become a real-life verb. On top of that, if it comes down to a brawl, he can kick guns out of hands with the best of them, and he's an accomplished mountain climber and ice hockey player.
Quinn Mallory in Sliders fits this trope perfectly.
Sam Winchester. While a badass demon hunter (it's a family trait), he's also brilliant at research, and had his girlfriend not been murdered, he was well on the way to becoming a lawyer. When it comes time to find out what's dropping bodies and how to kill it, it's Sam who finds out, but that's never stopped him from beating seven levels of ass or taking down all kinds of ugly monsters in hand-to-hand combat.
Bobby Singer. His home is full of stacks of ancient books that he uses for research (mostly to find things Sam can't find on the internet). And this little scene in Are You There, God? It's Me... Dean Winchester
Bobby: Solid iron. Completely coated in salt. One hundred percent ghost-proof.
Sam: You built a panic room?
Bobby: I had a weekend off.
Castiel. Admittedly, the audience (and Dean and Bobby) know from the very start that he's pretty damn badass, but to anyone who doesn't know who (and what) he is, he's an innocuous guy in a trenchcoat with a lot of esoteric knowledge and poor social skills.
Dean: He's tough, for a little nerdy dude with wings.
Walter White, from Breaking Bad. A high school chemistry teacher turned drug dealer, with a side order of explosives expert.
Michael Westen of Burn Notice. In addition to being rated on near "any weapon that fires a bullet or has an edge," he frequently gets out of situations by engineering some weird gizmo out of duct tape, paper clips, and a cell phone....that can blow a car full of snipers sky high. He also demonstrates, at the least, a rudimentary knowledge of finance, psychology, and chemistry. Comes with being a former CIA agent. It's mentioned he could've been his high school valedictorian...if it weren't for the fact that he a) kept fighting, and b) ran away to join the army at sixteen.
Barney from the Mission: Impossible TV show usually has a role designing gadgets or working complex machinery, but he is also often used for hand-to-hand combat. In one episode, he was revealed to have been a sixth fleet boxing champion, and while impersonating another boxer, wins several times against other skilled boxers without outside assistance.
Lennier from Babylon 5 is a highly intelligent, studious and soft-spoken aide, but he's also well trained in martial arts. He's highly skilled in combat and far stronger than he appears.
His opposite number among the Centauri mission, Vir Cotto, looks even nerdier and completely lacking in self-confidence, but even early in the series he is extremely competent and develops into someone more than capable of giving "The Reason You Suck" Speech to the Shadows' representative; going after a Drazi spy with a sword; assassinating the Axe Crazy Emperor Cartagia; and eventually taking the throne himself.
Cynthia from Malcolm in the Middle. While being both an adolescent girl and a huge nerd, her education extends to complete knowledge of Krav Maga, which she uses to disable Reese quite effortlessly on a couple of occasions.
Both of the main characters from The X-Files. Mulder is brainy enough to have graduated from Oxford, but his day job frequently involves outrunning men on horseback and fighting mutants. Scully tops off her undergrad physics major and medical degree with Improbable Aiming Skills, as well as doing more than half her share of the rescuing.
Mulder is actually a bit of a subversion, since Mulder and Scully were designed to invert traditional gender roles. Scully is an excellent shot and skilled (especially for her size) in hand-to-hand combat. Mulder, on the other hand, sucks at fist-fighting and loses his gun so much that he starts carrying an extra in an ankle holster and lampshades it. However, he is an excellent profiler and capable of making insane leaps of logic. He's more likely to use both to bring down his opponent without needing to physically kick his ass.
Temperance Brennan from Bones. World-class forensic anthropologist with improbable martial arts skills and a love of large-caliber weapons. She once took down a perp who had just shot Booth with a shot to the throat on the fly.
Fringe's Peter Bishop is supposed to be a con man, going through life on charm and a genius-level IQ. But it seems he hasn't neglected the physical side of his education: he's pretty good with a gun and has been known to demonstrate some serious ass-kicking when required.
Nick Cutter, a quiet, brooding, maverick scientist who can punch a Velociraptor in the face while reciting its biology, taxonomy, behavior and feeding habits.
Though he's had to take several levels over the years, Connor Temple is definitely this by the end of series 3. Especially if one makes the mistake of threatening Abby.
Abby herself arguably counts. She's a zookeeper and lizard biologist who gets rather pissed when her pet Coelurosauravus is being threatened.
Arguably Jess in Series 4 could be considered this, to some extent. Though not a typical 'bookworm', she's certainly the geeky team member now (aside from Connor), but even though she's just nineteen she has zero problems facing the creatures and anomalies themselves, and is described several times as being probably the best team co-ordinator the ARC could possibly have. She defuses a bomb (admittedly under Becker's guidance) and shows she knows how to handle a weapon, in her own CMOA.
Matt Anderson. He doesn't give much away, but he can identify prehistoric creatures roughly as well as Connor can.
The Sarah Connor Chronicles: While watching her beat up everyone, it's sometimes hard to remember that Cameron is incredibly intelligent. This is only natural, though, as she never sleeps, can read very quickly, and spends a lot of nights at the local university library just studying. Apparently, she gets bored easily.
Early in the first season, she mentions that she spent one night simply reading a dictionary from one end to the other. Also, in the episode "Self Made Man", she turns to full-on detective mode and tracks down a terminator no one even realized existed and had been hidden for the better part of a century.
Ianto is pretty much the epitome of this trope. He spends most of his time in the archives (at least in the first series), always knows pretty much whatever the rest of the team needs to know, makes snarky comments and puns, and doesn't seem particularly menacing. But give him a weapon- or hurt/threaten someone he loves- and he turns out to be quite the badass.
Djaq and Tuck from Robin Hood. Though both only get their hands on one book each during the show's run, they are clearly well educated and have a love of reading, and are debatably the most Bad Ass characters on the show.
The Twilight Zone episode "The Obsolete Man" has Mr. Wordsworth the condemned Meaningful Name librarian in a totalitarian state, who faces off with a state official to prove who has more courage.
Alias's Jack Bristow. He's introduced in the pilot as Sydney's no-nonsense father whose deadpan snark could cut glass, and "sells airplane parts". You'd barely trust this guy with your checkbook, much less international espionage. Fast forward to Sydney about to die in a parking garage, and Jack screeches up in his car, sticks his head and his Glock out the window, plays chicken with the assassins, and hightails himself and his daughter out of there. Oh yes, did he mention he's a Double Agent? Jack proves to be an icy-calm stoic game-theorist whose Chessmaster abilities in tandem with his physical abilities just make him even more dangerous.
How I Met Your Mother has Marshal Eriksen. He's a lawyer and a damn good one. He also has the ability to analyze and learn any type of board game or card game in quick order and then proceed to win at it. He's also 6'4" and can knock out an even bigger bar bouncer in a heartbeat, although he'd prefer not to.
Gabrielle from Xena: Warrior Princess is a bard by profession, always writing stories. As the series progresses, Gabrielle goes from innocent non-combatant to a highly skilled fighter in her own right who earns the Fan Nickname "The Battling Bard of Potidaea."
The Season 2 villain on Veronica Mars, Cassidy Casablancas, is characterized as being very intelligent, and his murders are neatly calculated, requiring no physical contact with the victims. This is in direct contrast to Season 1's Big Bad, Aaron Echolls, whose killing was an unplanned crime of passion that resulted from him being unstable and brutally violent.
Abby may be a lab tech but she can disable even hit-men in a melee.
McGee is a little bit of this as well. He's a field agent, which brings the badass part in the job description, but he's also the team's tech guru.
Sanctuary: Helen Magnus is most often seen utilizing her abilities as an Omnidisciplinary Scientist to solve problems and save the day, but her coworkers in the Sanctuary are always quick to point out that she can handle herself in a fight and she has shown the ability to do so many times. Her ability to kick Adam Worth's ass despite his ability to teleport is a good example. Monsoon is just an excuse to show off Helen evading the bad guys and the innocent bystanders through a combination of wit, stealth, and hitting people in the face. The following exchange sums it up quite well:
Charlotte: What are you, a spy, an agent or something?
Methos. Granted some of his bookworm-ness is his cover as a Watcher, but he still fits.
Aunt Marie from Grimm: a retired librarian and terminal cancer patient, she's also one of the last living descendants of Jacob & Wilhelm Grimm and her Airstream trailer has an arsenal, armory, pharmacopoea, and archive giving one the knowledge and tools to deal with vampires, werewolves, ogres, witches, trolls, jaegerbaern, and all other manner of nasties. She bequeaths it to her nephew, but unfortunately dies before she can teach him how to use it all.
Monroe arguably fits here as well. He's a multi-lingual clockmaker, chef, and musician who can literally dis-arm someone without meaning to.
Warehouse 13: Myka, Claudia and H.G. and Artie are all examples of this. The series is exceptional in that more of the heroes fall under Badass Bookworm than non-Bookworm Badasses.
Abed from Community occasionally displays remarkable physical prowess (usually exceeding his former-jock better half). He's easily beaten Troy in a footrace (without being visibly winded) and taught him a cool karate move by effortlessly slamming his head into a table (in an online minisode). Annie might also qualify due to her performance in paintball and when playing adorable bad cop.
Blair Sandburg in The Sentinel. Anthropology grad student, all of 5'8", glasses, strong aversion to guns. But he took out one terrorist with a restroom stall door and another with a vending machine; he cut through the floor of an elevator with a torch to drop a bomb down the shaft; while chained to a dentist's chair by a psycho serial killer he was able to verbally push all the nut's buttons to keep him off balance until rescue could come; he used a walking stick to knock a thug through a third story window; he subdued several criminals with a fire hose; he took on a shooter armed with a box of baseballs (and a great throwing arm.)
Emerson Hauser from Alcatraz was a philosophy student before he started on the law enforcement track that took him from cop to FBI agent.
While computer wizard Hardison from Leverage starts out as being less-than-imposing in a fight, he ends up more than capable of taking down guards in a one-to-one fight.
Archeaologist Matt Bellows from MythQuest takes out two armed Egyptian guards. When asked where that came from, he says, "You don't spend as much time as I do dealing with shady antiquities dealers without learning how to protect yourself."
Rumplestiltskin/Mr. Gold from Once Upon a Time has been working his way up to this, from the unremarkable peon hobbling around with a crutch, no discernable aggressive traits whatsoever and no options under attack but pleading and almost breaking into tears, to the Dark One, who still looks like a bantam weight but with plenty of magical knowledge, power and the nastiness to crush you under foot, rip your heart out or stop a war, to finally Mr. Gold: Fiftyish, (mostly) soft-spoken Pawn Broker with a limp who puppeteers the entire population of Storybrook (including one evil Queen) through his decade-long plans and shows a surprising ability to wreak havoc with that cane of his. The one thing all three have in common is looking like they have not one spare ounce of flesh on them.
Chuck Bartowski. Even before he gets the Intersect 2.0, Chuck's intelligence, resourcefulness and Genre Savvy allows him to outwit and defeat trained spies and hardened criminals practically at will. By the end of the series he's completely capable of kicking Shaw's ass even without the Intersect.