In the Gone series, Computer Jack is highly capable in computers... And kicking your ass. As of Fear this trope applies to Astrid as well
In The Lord of the Rings, Gandalf is incredibly wise and looks like an old man, but he mixes it up with the rest of the heroes with spell and sword. Faramir is another example.
"Nor were the 'loremasters' a separate guild of gentle scribes, soon burned by the Orks of Angband upon pyres of books. They were mostly even as Fëanor, the greatest, kings, princes and warriors..." The Peoples of Middle-earth, "The Shibboleth of Fëanor", J.R.R Tolkien.
The Silmarillion: Among the Eldar of House of Finwë were some of the brightest scientific minds in Arda's history, and they were also fierce warriors.
Prince/Shah Raschid in the Fangs of K'aath book series. He is a quiet scholar whom everyone thinks is a brainy wimp compared to his sociopathic brother, Abbas. However, with his wily girlfriend helping with practical matters of command, he displays his formidable combat, command and diplomatic skills guided by his good nature that make him a triumphant and inspirational commander of whole armies deeply impressed enough into absolute loyalty to him.
C.S. Forester's Horatio Hornblower who becomes a great Nelsonian seadog by his mathematical ability and his research skills. He also fights countless battles hand-to-hand, steals enemy ships by night, swashbuckles with the best, and duels a sadistic ship-mate who is so disturbed that he scares all others crapless.
Mr. Slant, zombie attorney and president of the Guild of Lawyers, whose death only made him work through lunch breaks. He can quiet a roomful of attorneys with a glance, and he has an encyclopedic knowledge of case and precedent because he was there and helped write it.
In Night Watch, a young Havelock Vetinari is bullied by his schoolmates in the Assassins' Guild for reading books with some interesting ideas about camouflage. Also chastised by one of his teachers for not being seen in any of his camouflage classes. He attended them religiously. Later vindicated when he manages to avoid the fate of the assassin who took the contract before him, the aptly named Sir John Bleedwell.
Most senior wizards, and of particular note, Mustrum Ridcully. He may seem stupid, but anyone who could get to be a level 7 wizard under the old system was either very smart, or very cunning.
Unseen Academicals gives us Mr. Nutt, a goblin who spent time in the libraries of Lady Margolotta (one of Uberwald's most powerful vampires) and damn near memorized them. He works as a candle dribbler at the Unseen University, and is extremely courteous, softspoken, and loquacious. He's also not a goblin; he's one of the last few orcs on the Disc. Orcs were originally bred as a super-soldier race for the Evil Empire. So when Mr. Nutt finally gets in touch with his orcish nature, he's able to tell an opponent he's got in a headlock just how much force it would require to rip his head off, and what muscles and bones would get in the way.
There's Ponder Stibbons, who rises by stealth to become effectively the third most powerful wizard on the Disc after Ridcully and the Dean. In Unseen Academicals, he lays the Lore down to both, with a vengeance. And they accept he's right.
Watch Adjutant Inspector Pessimal wields power. And he is feared for it.
Tiffany Aching may be only nine, but she's read the dictionary cover-to-cover, mostly because nobody ever told her not to. She also whacks a monster with a frying pan, befriends the Nac Mac Feegle, takes on The Fair Folk to rescue her unpleasant little brother, and studies witchcraft with the intent of stopping future witch hunts in their tracks. And this is just the first book she appears in.
Professor Abraham Van Helsing in Dracula. The fact that he has "M.D., D.Ph., D.Litt., etc" after his name yet still hunts vampires should attest to this.
Kirsty from the Johnny Maxwell Trilogy. In addition to having an I.Q. of 165, she's won a regional tournament in shooting and knows karate. The people who underestimate her tend to do so for a very short time.
Hari Seldon in the first Foundation prequel. Turns out his entire homeworld knows kung fu.
Adele Mundy in David Drake's Republic Of Cinnabar novels is a research librarian who is an expert shot with a pistol. She never misses, even in free fall, even if rotating in free fall from her previous shot.
The Sissies were proud of their Signals Officer: the lady who'd as soon shoot you as look at you, who knew everything, and who never missed....
Hogg - She cleaned out this enclosure. She did it. Tovera said she just walked in and shot them all.
Harold Lauder from Stephen King's The Stand probably qualifies, although it's somewhat subverted in that years of being bullied, ignored, and rejected leave him bitter to the point of using his considerable skills and intelligence for evil rather than good.
Wild Rhona from A Harvest Of War has written several books including a history anthology from which the book's opening quote is supposedly lifted. Other Wilds are shown reading in their leisure time. Still other characters are presumed to be well-educated, such as Guinevere Thyll and Ayan.
Holmes is a brilliant detective, violinist, and black belt. His scarecrow physique hides surprising strength. In "The Speckled Band," a villain tries to intimidate him by bending a solid metal poker with his bare hands. Holmes is unimpressed and casually straightens the poker afterwards while chatting with Watson. In "The Solitary Cyclist" he easily beats up an unruly suspect. In "Hound of the Baskervilles," he's noted as an extraordinarily fast runner. Some viewers of the Guy Ritchie adaptation criticized the film for making Holmes into an action hero, but feats like engaging in bare-knuckle boxing matches are actually canon for the character.
Watson is a marginal example. He is a practicing London doctor, but also an ex-soldier who holds his own whenever Holmes's adventures get messy. However, he's described as being rather handsome, so he probably doesn't look much like a weakling. Many film adaptations turn him into a pudgy goober without much combat ability.
And then there's Lord Peter Wimsey. Also extremely clever, he looks like an effete aristocrat (in Murder Must Advertise he's described as "Bertie Wooster in horn-rims"). He's slightly built, and only 5'9" tall... but he was also a highly decorated World War One veteran, judo-trained and capable of holding off large beefy antagonists on several occasions. He is also a champion cricket player, a brilliant detective, a great student while at Oxford, and a famous expert on incunabula.
Isaac Dan Der Grimnebulin, in Perdido Street Station: while he is supposedly just a rogue scientist, he holds off an attack by the corrupt government's trained militia and faces off against monsters so scary that demons are afraid of them. He's described as a fat and gets winded when walking up a flight of stairs, but he's also quite large.
Three of Doc Savage's five sidekicks qualify for Badass Bookworm: Elegant legal eagle "Ham" Brooks. The sickly looking, undersized "Long Tom" Roberts. And Professor "Johnny" Littlejohn with his monocle.
The Harry Potter novels feature many examples, since studying magic makes you badass.
Hermione Granger is a notable example, being a know-it-all bookworm whose studies grant her significant magical power. She comes into her own in the last book, where nothing would have gotten done without her hyper-organization and constant vigilance. In the films, she even slugs Malfoy in the face, though it's only a slap in the books.
Dumbledore, a prime example of how knowledge equals power.
Professor McGonagall and most of the Hogwarts teachers are all examples, being academics and experts in various fields of magic. Over the course of the series, there are hints every now and then, but in the final battle in Deathly Hallows, it's shown exactly why you do not screw with a Hogwarts teacher.
"Us teachers are rather good at magic, you know."
Laura of the H.I.V.E. Series is slowly but surely becoming one of these. While she doesn't have to use it very often because she always has Shelby with her, she occasionally displays an ability to aim and fire a variety of weapons competently and quickly. In books seven and eight, she is a student of the Glasshouse, where she trains in hand-to-hand combat. She isn't as good as some of the other students, but the fact that she even survived puts her well above average.
Atticus Finch of To Kill a Mockingbird follows this well. Scout actually calls him a wimp when compared to other fathers. He spent most of his time inside, reading and working as a lawyer and always giving fortune-cookie-ish advice to the kids. But when a rabid dog comes slinking into the neighborhood, he proves to be the best shot in the neighborhood. After this day, Scout never calls him a wimp again.
Aramis from The Three Musketeers: His life ambition to become a priest and his writing a thesis on the hand positions used for ritual blessings in the Catholic Church does not prevent him from being a member of an elite military unit and having martial skills on par with his less intellectual comrades-in-arms.
John Ringo really has a habit of placing badass bookworms in his stories
Into the Looking Glass, has William Weaver, Ph.D., a theoretical physicist who does most of his work in his head... while mountain biking, rock climbing, participating in kung fu tournaments, and fighting off an alien invasion. Except for the last, Ringo's co-author in the series after the first book, Travis S. Taylor, actually does everything attributed to Weaver, in Real Life.
Micheal O'Neal, a Sci-Fi geek who gets placed in charge of an ACS battalion. O'Neal mostly gets his position because he's the only one with a clue how to effectively use the ACS's, though he is described as being very powerfully built.
The Combat Engineers in Gust Front deserve mention for routing a Posleen force through creative use of demo. By the end of the book, the smart God Kings refuse to go near anything with an engineers' symbol on it.
In the first book, Sabriel is at the top of her class in every subject, most notably Swordfighting and Magic (with Music close behind), and, while well-liked, certainly gives very little indication to her school friends of her real powers.
The Aubrey/Maturin series features Stephen Maturin, a 5'6", gaunt, clumsy, "small, indefinably odd and even ill-looking" man as well as a doctor, polyglot, natural philosopher and all-round intellectual, and Britain's greatest spy. Over the course of the books, he is seen shooting the pips out of playing cards, winning several duels, operating on himself and dispatching his enemies in very badass ways. And then dissecting them. Yet, somehow, he never quite develops the ability to board a ship under his own power without falling in the water.
Parodied by the Chinese text of Lion-eating Poet in a Stone Den, where the title character is a poet who... kills and eats lions. It's more of a tongue-twister, mainly because all the words are pronounced the same, only with different inflections. Also, he's parodying the Chinese poets and authors as they were well-known for spicing up their characters, like in Journey to the West.
The Keepers of Brandon Sanderson's Mistborn trilogy. They primary goal has been to collect knowledge for a thousand years, only to give it back to mankind after the Collapse of the Final Empire. However, their feruchemicals power also allow them to store physical abilities (strength, speed, sight, etc...) to use it later. Making them very powerful warriors.
Then Sazed is not just any Keeper. In book 2, he kills a mess of koloss and nearly beats a Steel Inquisitor. In book 3, he becomes God.
Also Elend becomes this in book 3 after he becomes a Mistborn.
The avout of Anathem study logic, math, and philosophy their whole lives, which makes them the perfect people to storm a super-advanced "alien" space ship. This goes double for Fraa Lio and the avout of the Ringing Vale, who study the science of combat.
Snow Crash features Hiro Protagonist. He's one of the world's best programmers and shows equal skill in swordfights and car chases.
Casimir Radon from his first book, The Big U, a "skinny, unhealthy-looking nerd" who shows immense courage and near-superhuman strength in every crisis.
In Zodiac, Sangamon Taylor is an intellectual environmentalist and a bit of a thrill-seeker who throws himself into many dangerous situations and kills off a few hitmen with his driving and seamanship. Even on his daily bicycle commute, he plays chicken with heavy traffic.
Strongbow Plantaganet from Edward Whittemore's Jerusalem Quartet.
Snowball from Animal Farm is very intelligent, designing a windmill and setting up committees and leading the animals to victory in The Battle of the Cowshed, where he sent Mr. Jones into a heap of dung and was wounded in the process.
Barrons from Karen Marie Moning's Fever Series. He owns a bookshop, is named after a publishing company, and is pretty mysterious and badass, with being immune to shades, Living Shadow and all.
Almost every Robert A. Heinlein character ever. If they don't read advanced math at the beginning of the story, they either get really into it just in time to defeat the Space Nazis using calculus and Latin, or die.
Tom Clancy's Jack Ryan in The Hunt for Red October and other novels. He is a quiet academic whose job and hobby is to study naval trivia for the CIA. However, he manages to win a shootout amidst a Pile o' Nukes, and beats up a bunch of Irish terrorists with his bare hands.
Annabeth from Percy Jackson and the Olympians reads architecture books in Ancient Greek at the age of twelve. She is also a brilliant but brutal strategist and fights with a bronze knife. We guarantee that she can kick the butt of almost any mythological creature you care to name. Daedalus is also a brilliant swordsman who also happened to create the labyrinth, the most brilliant piece of architecture ever.
Stephen King and Peter Straub's Black House features a whole gang of bikers each with master's degrees in philosophy who own and operate a microbrewery with full knowledge of the chemicals processes at work. They're still badass enough that most of the town knows to leave them the hell alone.
Soon I Will Be Invincible's Dr. Impossible. He's the smartest man in the world and not particularly intimidating physically but is superhumanly strong and tough.
Henry from The Time Traveler's Wife would like to be just a simple librarian, but his chronological-impairment tends to leave him in situations where he needs to mug people for pants. As such, he's managed to become very good at beating the crap out of people. (He's mostly self-taught.)
Harry Creek from John Scalzi's Android's Dream universe arguably counts. Born a geek, raised a geek, created the world's first (Well. Second.) artificial intelligence, oh, and also survived one of humanity's worst military excursions, and managed to bring an opposing stellar government to its knees by surrendering.
The Andalites from Animorphs are a species of badass bookworms. Members of their military are expected to embody the ideal of "scientist, warrior, artist."
Tyrion Lannister is a bookish dwarf with no love of physical exertion, but he goes into battle twice, once taking down a knight by accident and in the second performing great feats of heroism.
It is also hinted that Petyr Baelish, a short, noncombatant financial genius, is an expert with knives and fairly nimble on his feet.
Rhaegar Targaryen was well known as a reclusive, scholarly prince who one day out of the blue decided to take part in a tourney against the best knights in the kingdom... and won, despite only ever reading about tourneys. He then promptly ran off with the protagonists' sister, unintentionally helping to set off a Civil War (though his Caligula dad did most of the work by killing some nobles in horrible fashion for no reason) by pissing-off her betrothed, hot tempered Action Hero and future king Robert Baratheon, and the only man in Westeros who doesn't think Rhaegar was the most awesome Bad AssWorthy Opponent who ever walked the Earth. The two eventually fought and though Rhaegar lost, he is said to have fought valiantly and bravely in a truly epic battle.
Samwell Tarly. Chides himself constantly for being cowardly, fat and useless. Yet, he actually manages to kill an Other. By accident, but still. Also, his extensive knowledge makes him into a non-combatant badass, either way.
Professor William Race from Temple is brought on a secret mission to translate an ancient manuscript. Somehow, despite having no military training, he gets dragged along to every battle and ends up being the last man standing.
Humanity as a whole fit this trope at the opening of the first Man-Kzin War. Having become intellectual pacifists, humanity is viewed by the Kzinti as weak and cowardly... except humanity had given up war because they were too good at it. Four destroyed battle fleets later, the Kzinti finally started to catch onto this.
Ivy from The Dresden Files is a seven year old girl who fawns over Harry's cat in her first appearance. She's also The Archive. She has the sum total of all human wisdom and knowledge floating around in her head, updated live. Since knowledge basically equals power in the series, she has a lot of power, enough to literally reduce multiple Fallen Angels into dust while under a severe handicap. Most people in the know consider her to be one of, if not the, most dangerous human magic users on the planet.
Wizards in general. Harry has on several occasions described himself as a "magic nerd". Most of these folks spend a hundred years or so learning how to lay some serious hurt on anyone in their way. For all intents and purposes, despite all of the incredible feats that Harry pulls off throughout the series, he's still an amateur.
Special mention goes to the Merlin of the White Council, Arthur Langtry. He is, quite simply, the most powerful wizard on the planet. In Dead Beat, Harry is told that the Merlin held off the entire Red Court with an impromptu ward.
Harry Dresden: You don't get to be the Merlin of the White Council by collecting bottle caps.
Tim Noonan is the Gadgeteer Genius of Rainbow Six, but he was also "poached" from the FBI's Hostage Rescue Team, as we are reminded from, among others, his quick takedown of PIRA terrorists during their attack on the hospital.
El Grecans might have been highbrows and philosophers, but that hadn't meant they were airheads, and the Rish soon discovered that they'd caught a tiger by the tail. The academics of El Greco warmed up their computers, set up their data searches, and turned to the study of guerrilla warfare, sabotage, and assassination as if preparing to sit their doctoral orals. Within a year, they had two divisions tied down; by the time the Sphere gave it up as a bad deal and left, the Rishathan garrison had grown to three corps...and was still losing ground.
Brandark Brandarkson from the The War Gods series is another David Weber example. Brandark grew up in a place where literacy or any sort of education was considered a sign of weakness. Therefore, the only way he could survive as a bookworm was to be so badass he could beat up anyone else in his clan.
In Bram Stoker's Dracula, Jonathan Harker had been a quite ordinary young lawyer from London until his life and death (or to put it better, undeath) were at stake. It takes some badassery to escape while locked in a castle populated by vampires and then hunt the vampire boss himself throughout Europe. With a Kukri nevertheless.
Numair Salmalin. University-educated in Carthak, The Archmage of Tortall, and so absentminded he might accidentally put you under a mild hypnotism just by staring at you.
In Protector of the Small, Kel's best friend Nealan of Queenscove is a biggie. He was studying at the university to be a healer before he switched to knighthood, so he's incredibly knowledgeable and trained in debate technique to boot.
And in Daughter of the Lioness, Dovesary Balitang. She might not be an Action Girl, but she's so sharp and politically savvy it becomes badass. If she does need to put down her book, she's quite good at archery. As Prince Bronau discovered.
Derek Vandaveer of The Zenith Angle by Bruce Sterling is primarily a computer science geek specialising in networks, but well able to handle himself in a fight and undertake illegal black ops. Part way through the book he spends a lot of time working out his frustrations on an exercise machine, so maybe he's taken a level in badass, but there is a strong implication that the underlying attitude was there all along.
The Collegia Magica trilogy by Carol Berg has some prime examples: Portier has been described as a walking encyclopaedia, Dante, the strongest magician in 200 years is a self confessed bookworm and Anne, potentially stronger than Dante in magic, knows seven languages and can describe theories of gravitation and optics in detail. Oh, and loves to read.
Randolph Carter in HP Lovecraft's Dreamworld stories, a scholar who repeatedly goes up against horrifying creatures. While in his first story, "The Statement of Randolph Carter", he's described as a nervous wreck, Lovecraft actually Ret-Conned that in a later novella, "The Silver Key", where Carter is described as having PTSD at that time — he'd been shot in WWI while serving with the French Foreign Legion.
Both Tavi and Ehren from Codex Alera count. Neither of them are very physically imposing—well, Tavi isn't until his twenties, though Ehren remains a self-proclaimed glorified "messenger boy" forevermore—and both of them are less then talented with the world's magic. However, both are extremely intelligent and kick much ass as they're much stronger than they are allowed to let on. For example, Tavi beats a couple of powerfully gifted bullied senseless without any furycraft; he's also told by an instructor to mimic the mistakes his classmates regularly make so that they'll be more vigilant about them because his own skill is sufficiently advanced. Ehren becomes a bit of a knife-nut, a spymaster, and a chessmaster.
Gen from The Queen's Thief books; he's small, lives in a library, and is much happier when he is skulking about and stealing things than when he's forced to practice any sort of martial art. However, he's a master swordsman, able to take down in an instant alone three assassins who ambushed him, and also able to spar with and beat a good portion of a company of elite guards in a single morning. Also, he as a hook for a hand, and uses it to deadly effect.
John le Carre's character George Smiley. He's a portly, middle-aged man whose eyesight is going, and whose wife gives him more than his fair share of problems, yet he was one of Britain's very best spies in his prime. He's still badass enough for "the Circus" to call him out of retirement when they need help in finding a mole. His skills are more in his gift for bureaucratic trickery, however, than any physical prowess.
Schooled In Magic: Emily is a neglected young girl who found safety in the library. She especially loved books of history. When she was taken to a fantastic world of magic and dragons, her love of reading became a huge advantage to her as she is now equipped with knowledge that will change the world and give her great power.
Scaramouche: Andre-Louis Moreau, a lawyer, discovers - from studying fencing theory - a technique that will defeat even the most experienced opponents.
The Decepticons have Razorclaw, a diminutive wolf-former who is The Professor and a Team Dad/Mentor who likes to lecture his two students. When it's time for battle, though, he's ferocious and quite capable of ripping the heads off of Autobots much bigger than he is.
And the Autobots have Blurr, a Wicked Cultured ex-professor who's usually very calm and unassuming, but is a member of Optimus' elite attack squad and can absorb kinetic energy to become a quick and deadly warrior when needed.
And in the G1 cartoon spinoff Transformers: Wings of Honor, when the Elite Guard finds itself low on members, they take in two "desk jockeys" as volunteers—one of which turns out to also be a sharpshooter, and the other of which once dispatched Decepticons using a desk stapler.
Toni Ware and Leonard Stecyk in The Pale King. Thanks to spending childhood as a drifter, Toni is well-read but borderline homicidal. Leonard's extensive knowledge of medical techniques helps him saves someone's life and jump-starts his character development.
Time Scout: As a rule, time guides and time scouts have to be very, very knowledgeable about the past. Clothes, weapons, language, dialect, accent, dancing, fencing, fighting, shooting, riding...
Leland de Laal, the primary protagonist of Steven Gould's Helm, was generally held in contempt by his father for spending every spare moment of his time studying in the library — until, at the start of the book, in defiance of his father's proclamation, he scales a three-hundred-plus meter high granite formation known as the Needle solo to take the titular Helm that rested atop it. His feats only grow more impressive from there.
The "Four Horseman" — a quadruplet of small-town D&D nerds, wargamers, and dirt bikers — in 1632. Jeff Higgins in particular reveals his exceptional poise under fire starting with the Last Stand in the high school and escalating from there. Even his glasses add to his badass cred, to downtimers: they believe that they enable him to see his victims better, instead of more modern general interpretations of glasses wearers as being wimpy.
Aziraphale in Good Omens - despite his mild, kindly, book-obsessed exterior, he's actually a sword-wielding angel who's been on Earth for the last six thousand years, has seen everything at this point, and ends up going against Heaven's own directives in an attempt to prevent the apocalypse from occurring, despite all of Heaven and Hell being pro-Armageddon. Oh, and he's sort of secretly best friends with a demon, Crowley.
Rafael in Gives Light. A bit of a subversion, because he's not smart as the trope would ordinarily entail. Instead, he comes across as a bit slow witted. Also doubles as Badass Gay.
All the wizards in The Black Company fall into this category, especially the Taken. The setting averts Squishy Wizard, hard. One particular Taken has a building collapsed on him and survives without permanent damage. A later scene has a single Taken fighting off his attackers while outnumbered five to one and treating the severing of his right arm as little more than an inconvenience. It's noted that a different Taken eschews physical weaponry entirely, knowing that his sorcerous talents afford all the protection he needs. Bonegnasher is another Taken, a One-Scene Wonder who is described as a giant man who is shown fighting his foes by tearing them to pieces with his bare hands.
Croaker himself probably counts, as well. What time he doesn't spend writing the Company's annals, patching up the wounded, or studying ancient documents, he spends either playing cards or fighting on the front lines (despite being in his forties by the start of the second book, though he notes that he prefers to be an archer who's out of the thick of the fighting by then.).
Simona Ahrnstedt gives us Beatrice Löwenström in her debut novel Överenskommelser. While she is an intelligent book lover, she also competes with men in ice-skating and horse-riding, assists in a surgery and calls the villains out on their atrocities.
Serah in Rogue Sorcerer starts out as just a bookworm, but she grows into quite the formidable fighter by the book's end.
In Lois Mcmaster Bujold's Chalion series, in the first book stars Cazaril, who is a Broken Bird and tutor to the Royesse Isselle and her handmaiden, who wants nothing more than a quiet life, a chance to read and perhaps write undistinguished poetry. He's also a former soldier who has marched the length of his nation and back again in a series of wars that have drained it and left him betrayed and sold to the galleys for two years, making him a deadly The DeterminatorCombat Pragmatist who will stop at nothing to protect and serve "his ladies".
Journey To Chaos: To be a mage in this univese, you have to do a lot of studying. That fireball spell requires a working understanding of mana and the basics of how fire operates. Over the course of A Mage's Power, Eric learns to do just this and more.
The Goblin Emperor: Cala is even-tempered, kind, and often implied to be absorbed in his studies when he's not occupied with guarding the emperor. He casts a death spell on a would-be assassin.
Jimmy in Salsa Nocturna who is a high school age nerdboy genius and does research as he learns about the world he now inhabits.
Dro in Half Resurrection Blues who is equal parts researcher and warrior.
Sixtus Claudius Julianus, a character in Search The Seven Hills is over seventy years old and lame, long retired and isolated inside his big, deteriorating mansion writing a work on Eastern Cults. He can also take down two healthy, armed men less than half his age in less than a minute.
Christian Ozera from Vampire Academy. His intelligence is mainly spotlighted in the first novel, when he figures out the nature of Lissa's magic. He is very intelligent and observant, deducing things out of simple clues. He proves to be badass in Shadow Kiss, when his fire powers kill many Strigoi.