Aizawa Kouichi from Nabari No Ou is, for all intents and purposes, that one kid with the glasses — smart, somewhat nerdy, nice, and almost boring in the shadow of his weirder friends. Yet he's revealed to be the most professional and capable ninja in his village, and is more than willing to kill/brainwash the influential (including the CEO of a vast, international medicine/defense technology corporation) if the mission calls for it. To be fair, he's actually not exactly human, or a middle schooler, having been created as a living experiment centuries ago.
Think twice before attacking Faust VIII, from Shaman King. Enjoy your vivisection if you do. He can operate a bone transplant on himself in the middle of battle. Now that's badass.
Nami, the cartographer/meteorologist who's also the Action Girl who actually uses the Clima-Tact created by Usopp. She uses it's ability to generate heat, cold, and mild electricity to cause powerful localized storms, or even to create mirages, due to her extensive knowledge of geography and weather physics. Even without the Clima-Tact she's formidable. In her first appearance she steals a ship from some pirates, timing the weather perfectly so that the oncoming storm sinks the little ship she left them in without sinking her new (only slightly larger) ship.
Klahadore/Kurahadol is introduced as Miss Kaya's unassuming, well-dressed butler. Early on he's shown to be incredily gentle and possibly bookish, as he constantly has to adjust his glasses. He's secretly a massive badass named Captain Kuro, who to his credit, still wears those glasses and was pretty well-dressed when he was a pirate. Acknowledged as the second smartest character from East Blue by the series' creator, he's a genius whose nickname is "Kuro of the Thousand Plans." And besides being a mastermind when the gloves come on (his Freddy Krueger-sque clawed gloves) he's also an incredibly powerful pirate who can move fast enough to vanish in front of people. Oh yeah, plus he zero respect for human life and plans on murdering his entire crew after his latest plan, a pirate attack on the village culminating in the death of Miss Kaya so he can inherit her fortune), is completed. He also faked his death by framing a look-a-like via hypnosis
Kiyomaro Takamine of Konjiki No Gash Bell, middle school student and master tactician with loads of stamina.
Kazuo Kiriyama from the Manga version of Battle Royale is an evil version, a sociopathic genius who spent most of his time quietly reading books and staying out of everyone's way. Due to this their gym teacher, a former Olympic Judo champion, decides to pick on him for a bit of a laugh, failing to notice that he's been reading a book on martial arts and looking remarkably confident... plus Kiriyama's first meeting with the guy who became his lieutenant. A book on anatomy and no human compassion equals the most ridiculously violent high-school beatings ever captured on a page.
Yuki Nagato from Suzumiya Haruhi is usually quiet and unassuming, and rarely ever puts down her book, even when everyone else is playing around... or when she's playing around, or even when she is water skiing. However, whenever she's confronted by the weirdness brought about by Haruhi Suzumiya herself and her Reality Warper power, Yuki exhibits surprising battle abilities. Such as the ability to temporarily overwrite reality, or play a bitchin' guitar solo. Her badass-ness is one of the reasons why she's not creepy. Her fight with Ryouko Asakura was great. Not only was she stabbed straight through by multiple objects, she was able to be graceful while doing it. She won that fight, actually.
Given that her true identity is that of a highly, highly advanced robotic interface, whose job is to gather information for The Data Integrated Thought Entity (an Eldritch Abomination), her mastery of data is very fitting. In later books, after Kyon assists her in slipping the leash a little, she becomes badass enough to break away from her own creator, and form independent emotion.
Gundam has a few:
Uso Evin likes to learn as much as he can, and his friends know that is usually near books when he is not piloting Gundam's. If he doesn't have a gundam nearby he just Gundam-jacks mid-air the nearest mobile suit.
Paptimus Scirocco is the poster boy for the villainous Bookworm: an ambitious political mastermind and Ace Pilot to rival Amuro and Char, he disdains social interaction and seems at his most content when he's working on his mobile suits or perusing data in solitude.
Kira Yamato has a habit of completely rewriting his mobile suit's operating systems in seconds, optimizing in mobility, and weapon performace, and constantly tweaks them to counter-balance with his location and surroundings. Did I mention he does this in mid-combat?
Flit Asuno completed his mother's mobile suit design, thus building his owngundam. He also didn't intend to pilot it, but did end up being the very first to beat a UE Veigan mobile suit as well as destroying every single Ace Custom in his path, and in the second generation, he may be a fleet commander but his home office is still filled with books.
Vivio, who became a librarian in the Infinity Library in third grade, begins showing more of her fighting skills in Magical Girl Lyrical Nanoha Vivid, including her skill in the Strike Arts style of martial arts, sparring evenly with Nove. This comes off as a surprise to Rio, who had thought of Vivio and Corona as "more of bookworm types."
Nanoha herself qualifies. The reason she's a Person of Mass Destruction at age 9 is that her math skills and intelligence allow her to perform really powerful magics. Out-thinking opponents doesn't hurt, either.
Eccentric inventor/businessman Kisuke Urahara, who used to be 12th division captain. He designed a method of achieving Bankai, a formidable power that takes years to achieve, in three days and was the only one capable of this until Ichigo. He has also been known to pitch his numerous inventions in the midst of battle. Aizen, a frightfully villainous version of the badass bookworm, acknowledged Urahara as the most intelligent person in the story.
Uryuu Ishida is top of his school class and student body president yet one-shotted both a Shinigami captain and his Bankai with a single arrow at the age of 15. In the final arc, Yhwach is so concerned about the threat the now 17-year old Uryuu presents that he kicks Uryuu upstairs.
Ryuuken, Uryuu's father, was so intelligent as a teenager that he took even Urahara by surprise. He is now director of Karakura General Hospital at a ridiculously young age. He is so powerful that he makes his extremely talented son look like an amateur.
Nanao Ise, Shingami lieutenant and member of a famous reading club in Soul Society as well as the Shinigami Women's Association. She gained lieutenant rank due to her formidable kidou skill, which is so good she could design a brand new kidou in only a day or two that was capable of repelling even Haschwalth.
Risa Yadomaru used to be a lieutenant prior to losing her position as a result of hollowfication. Hollowfication increased her power from what it used to be making her more powerful than a normal lieutenant should be. Her mentoring of Nanao when Nanao was very young is responsible for Nanao's love of books.
Momo Hinamori is a Shinigami bookworm who often partners Nanao for reading sessions. She's also a lieutenant who is an expert kidou master. Aizen spent years messing with her mind to ensure she had a powerful Heroic BSOD so that she couldn't be as effective as she should be when his villainy was revealed.
Shikamaru Nara from Naruto. What do you get when you give a ninja an over 200 I.Q.? Almost all of his fights involve him showing surprising quickness to dodge his opponent's attacks all the while analyzing their every move. And then deciding always on the correct counter strategy. Characters go through some pretty serious, near-fatal injuries in battle (Naruto even lost a lung), yet to date, Shikamaru's most severe battle-related injury that we know of has been...a self-inflicted broken finger.
All of the smarter ninja in this world count as this trope; on account of them being, you know, ninjas. Learning ninjutsu actually requires a lot of study and intelligence itself. Naruto himself, a prototypical dumb hero, demonstrates some pretty decent strategic thinking when the need arises.
Kakashi Hatake. Naruto calls him "as smart as Shikamaru which, combined with his status as the most elite ninjutsu specialist in the Hidden Leaf, would make him this easily. Inverted with his actual choice of literature- Jiraiya's erotic novels.
Sakura was introduced as an actual bookworm, and while one of the weakest of the Rookie 9, she is still a trained killing machine who demonstrates Improbable Aiming Skills and can kick a normal persons ass, she once let herself be hit with shuriken to get at an enemy. Post-skip, she has gained Super Strength and is a medical prodigy capable of inventing cures to elaborate poisons on the fly, before helping an old hag nin fight and kill the S-Class criminal who invented it. She is also hinted to have a talent for Genjutsu, which according to Jiraiya is a fairly intellectual branch of the ninja arts.
Orochimaru is a Mad Scientist who has pushed the boundaries of Forbidden Jutsu- including achieving a gruesome kind of immortality- and may have been on to the secrets of the Big Bad Uchiha Madara in the process. He is a fairly competent strategist- if Sarutobi didn't have that one jutsu, he probably would have destroyed the Leaf Village after all, one way or another-, has his own village where he conducts numerous horrific human experiments, and probably personally trained most of the younger Sound nin himself, as well as probably "modifying" them too. His Dragon, Kabuto, is a talented medic who has spliced his genes with Orochimarus' DNA.
Tsunade is a revolutionary medic-nin who now runs the entire Leaf village. And Jiraiya, arguably the most capable of the Sannin, is a best-selling author as well (of smut, but still...), and seemed pretty knowledgeable of ninja history.
Sand puppeteers like Sasori, Kankuro and Chiyo are expected to make and repair their own puppets, which are often elaborate death machines requiring a fair amount of maintenance. Sasori and Chiyo are both master poisoners as the weapons of the puppeteer are usually coated in poison, and Chiyo appears to have some medical knowledge as well. Sasori used to work with Orochimaru and it is implied they performed experiments together. And he's an artist, or regards himself as such at any rate.
The Akimichi clan secret jutsu rely on knowledge of special medicines; the Aburame are bug experts who turn their bodies into bug nests; the Inuzuka appear to be decent vets; and the Yamanaka...er, sell flowers.
Iruka. Chuunin-level academy teacher. Capable of projecting two sophisticated, all-senses illusions on opposite sides of Konoha. Echolocation (a possible bloodline limit). Can handle repeatedly being kicked in the spine by a beyond-super-strong former best friend. As skillful as Anko. Stood up to Pain.
Played around with the Data Tennis players (Sadaharu Inui of Seigaku, Renji Yanagi of Rikkaidai, Hajime Mizuki of Saint Rudolph, Taichi Dan of Yamabuki and Koharu Konjiki of Shitenhouji) from The Prince of Tennis. All of them use the information they collect to further their playing strategies (hence the "Data tennis" name), but the results are different since they have very distinct personalities and methods.
Inui and Yanagi also qualify in the Genius Bruiser category, both being over 6 ft. tall.
Her Badass Bookworm status is lampshaded by Ami herself in the Stars season, when Haruka chides her for prioritizing the analysis of the rival they're fighting over her own safety and Ami replies "This is MY way to fight!"
In the manga version Mamoru Chiba/Tuxedo Mask who graduated at the top of his class, is considered almost as smart as Ami, if not as smart, is an excellent fencer, and is also considered one of the best hand-to-hand combatants in the series. Pity the poor guy is still subjected to The Worf Effect even then...
L of Death Note, who is laconic, lazy, a brilliant detective, and quite able to hold his own in the occasional fistfight with Light. Must be all the sweets. In the third live action movie he uses a thrown hammer to knock out a Psycho for Hire.
Izumi is another splendid specimen -though it mainly happens offscreen, she must have studied like hell to get her alchemical know-how. But the most obvious case is probably manga Hohenheim: he's shown as a nerd of unspeakable proportions who spends more time in his study than with his family, lives on his own little nerdy planet and hardly ever fights. But when he does, it automatically results in Crowning Moments Of Awesome.
How about we say ALL alchemists fit? Since you know - even if we don't see Roy leafing through books too often he is an expert with his own alchemy, has a vast knowledge about other fields than his fire-thing - oh, and he is in the army. Which implies he is not only Bad Ass but also anything but Book Dumb .
Playwright prospect, Kaleido Stage fansite webmistress, very skilled with technical stuff as well as with literature-related knowledge, and a talented acrobat and actress on top of it all... That's Mia Guillem from Kaleido Star to you.
Rider in Fate/stay night, when you found out that she actually loves literature, when she is in her Meganekko mode. Combined with her already powerful abilities...
Kuroo Hazama aka Dr. Black Jack. Apparently, obtaining his Medical Doctorate has transformed him into some sort of surgery-performing ninja. This is the only way one can explain feats such as using scalpels to deflect bullets, or climbing across the surface of an airplane in mid-flight. Perhaps he wasn't really mentored by Dr. Honma, but by Dr. McNinja.
Inspector Heinrich Lunge. While being a ridiculously intelligent BKA investigator with a photographic memory is impressive, Lunge's real threat is that he's practically a human terminator who doesn't shoot to wound so much as he shoots to cause excruciating pain.
Johan himself. A bona-fide genius- he once posed as a Law student, but legitimately got all A's, in between advising a tycoon on how to run his financial empire whilst the two discussed Latin- who happens to be a super-prolific Serial Killer, a man who amongst other things slaughters entire families off-screen. He has hardened criminals, mad scientists and Neo-Nazis all worshipping the ground he walks on, and the rest of the world p*ssing themselves in his presence because he just oozes evil. He is utterly fearless (even inviting) in the face of death and has been shot in the head twice and survived. His hobby is walking the edges of skyrise rooftops and he is probably The Antichrist. Not known for his fighting skill, but he's pretty familiar with guns and was bred to be The Übermensch. He is also a Manipulative Bastard of the highest order and seems capable of talking civilization into destroying itself.
Negima! plays this by translating the Library girls' abilities into battle magic. Given that said Library is filled with death traps to the point where the ground floor is off limits to Jr. high students and below the 3rd sub-basement is off-limits to the university students, rock climbing gear is needed to get to some parts of the Library that is open to the public, one of the librarians is a top class mage, and there is a dragon in the basement, a case can be made that they were fairly badass even before starting to learn magic.
Even without that Teen Genius Yue was already clever enough to begin with to qualify. She actually manages to defeats a dragon/griffin hybrid after two classmates by leaping in front of them to block an attack,using her artifact to look it up, determine its weaknesses, and coming up with a plan that involved her stabbing a spot a few centimeters square with a small knife while dodging friendly fire.
And also, Albireo "Ku:nel Sanders" Imma, who qualifies as a badass librarian.
Nodoka Miyazaki is taking this trope and running with it in the last arcs with the way she is Min-Maxing her artifact. She is scary. According to Nodoka, ancient crypts and ruins in the Magic World are no match for Library Island. Nodoka's artifact is absolutely no help in dealing with traps, locks, or natural hazards - it's all her.
Isuzu Ayane from Gate Keepers 21 is quiet, ranked third in the second year level of her high school, spends most of her time reading and sitting in front of her laptop, and yet when it comes to her part time job, effortlessly takes down scores of Invaders by throwing cell phones at them.
In Ghost in the Shell, Ishikawa gets his Badass Bookworm moments near the conclusion of each season. The first time, he proves that he is definitely not a Technical Pacifist, by blowing up a building with his pursuers in it, and in the next season by bludgeoning a secret agent into unconsciousness with the cast on his broken arm so that he can safely deliver a rod of weapons-grade plutonium.
Walter 'Angel of Death' Dornez from Hellsing, a polite elderly monocle-donning butler whose WWII experiences happen to include tearing whole armies to shreds with monofilament. He can still do that, as he eventually proves with spectacular scenes of gore and destruction.
Appledelhi, Ed's father, from Cowboy Bebop is a geologist studying and mapping the ruined Earth, and a bit of a Cloudcuckoolander to boot. When he is forced into a confrontation with Spike, he effortlessly beats off all of Spike's attacks, and is well on the way to stomping him good when he's interrupted.
The Cloudcuckoolander part? The earth he's mapping is STILL BEING RUINED by rocks falling from the sky. Every time one lands he races off to map the changes. And like Ed, Appledelhi can take somewhat cartoonish amounts of abuse and shrug it off. In a show that, for the most part, obeys all the laws of physics. A show so based on reality that Spike uses a known martial art—Jeet Kune Do, as created by Bruce Lee. Sure, the Bebop crew run into some pretty strange occurrences, but Spike is strictly Badass Normal, ending the episode several times wrapped up as if he were a mummy. He is... outclassed several times.
Maka, the protagonist, is a recognized bookworm, a very badass bookworm that will kick your ass with her scythe-partner if you get in her way. She also packs quite the punch, too.
Ox Ford would probably count too.
Dr. Franken Stein likes to research and experiment, on himself as well as others. He is also the most powerful meister the DWMA has ever produced. His physical skill and soul wavelength abilities make him dangerous enough unarmed. Give him a Weapon, however, and he'll reallystart having fun.
In the 3rd episode of Golgo 13, the titular hitman is in a sniper duel with two mercenaries using advanced rifles superior to his own M16, and modified with a unique electronic "super scope". Based on their firing patterns, he deduces that the scopes have a vulnerability in that they do not take shifts in gradient into account. He then calculates the gradient necessary for their shots to be inaccurate, and positions himself in an area of the battlefield with that gradient, easily blowing them away. Duke Togo- international assassin, and math nerd.
Hakkai from Saiyuki, the polite and scholarly type in the party heading west. He even wears a monocle (if for different reasons). And then there's the matter of his energy blasts ... His past life Tenpou from Saiyuki Gaiden is actually a bookworm (to the point of being shown buried in books) and bespectacled, but people know very well you don't want to get him mad. He also single-handedly does the work of a military unit.
Tsutomu Tanaka, a minor character from Kenichi: The Mightiest Disciple. This 18 year old Salaryman with a young daughter first appears as a diminutive wimp who is fairly well whipped by his wife and boss, up until he stabs his index finger into a man several times larger than him without any resistance, KOing him instantly, and outruns a member of YOMI so fast that by the time she turns a corner, he has already disappeared.
Don't mess with Akira Shirase. Yes, he does look like a textbook example of computer nerd, who haven't shaved, washed or got enough sleep in three or four days. He also can listen to a song and write a binary of mp3 of it out of his head. He can also hack your PC into going boom using nothing more than a cellphone with internet connection. Or hack and drop a sequence of decommissioned spy satellites on your head. So, yeah, don't mess with Battle Programmer Shirase.
Manabu Yukimitsu from Eyeshield 21. Scrawny and weak, the only thing that even lets him join the team is the fact that he's more of a Determinator than the character whose determination is a running gag. However, after finally being put into the game against Shinryuuji, he manages to outsmart giftedJerk Jock Agon Kongo and score a touchdown.
Seto Kaiba of Yu-Gi-Oh! is one of the top two Duel Monsters duelists of all time, a master chess player, CEO of the world's most successful game company, and inventor of the Duel Disk system, among other high tech gaming gadgets. Oh, and he was also apparently trained well in Krav Maga, and can disarm someone with a card fling.
Seta Noriyasu of Love Hina is a university archeology professor who is something of a parody of Indiana Jones. He's also a remarkably skilled martial artist and (in the anime, at least) passes on some of this knowledge to Keitaro.
Kyrie Ushiromiya of Umineko no Naku Koro ni. Sure, she knows her place in the family conferences (near the bottom) and will leave most of the arguing to her husband Rudolf. But stick any kind of demon in front of her and watch it go flying. George may also qualify in the fourth arc, but Kyrie is more consistently this, and her analytical nature is way more played-up.
Anyone who does truth duels with any level of skill has to be this by sheer necessity. Battler, for example, refuses to call himself well-read because it would be arrogant due to "only reading about a hundred a year."
Harumi Fujiyoshi of Sayonara, Zetsubou-Sensei is a Yaoi Fangirl who spends much of her time producing doujinshi. However, she's also a very competent athlete and the school's sports teams often try to force her to join. One episode indicates that her glasses are a Power Limiter, and she'd be an even more amazing athlete without them.
Legend of Zelda: Four Swords+ : Vio is Link's "smart side" and is often seen reading. And yet, he's still strong and skilled enough to beat the "original" green Link in a sparring match.
Manabizaki from SWOT is a person who studies too much (which is what the title means). He's always found with his nose buried in a book. However, he also has a Hair-Trigger Temper and gets really pissed when anything interrupts his study time. This attitude, coupled with his externally nasty behavior, have gotten him into fights with delinquents... to their detriment.
Gohan was raised his whole life to become a scholar. Despite being a straight-A student, Gohan is one of the strongest fighters of the show, even having more fighting potential than his father. Even after spending a decade doing no martial arts training and not fighting anybody more formidable than random unpowered criminals, he's still capable of effortlessly kicking the ass of well over 99% of all fighters in the universe, and is stronger than God.
And then there's Piccolo, who is simultaneously the Big Guy and the Smart Guy of the Z Fighters.
Black from Pokémon Special. Is he a Large HamDeterminator with Hyper Awareness? Yes, but he actually did some research before he went on his journey, and outright states that he's been spending time reading in libraries ever since he was a little kid so he could learn everything he possibly could.
Preceding Black is PlatinumBerlitz who reads 10 books a day and knows quite a lot of concrete facts about Sinnoh, and various facts about a wide range of disciplines despite never leaving her mansion.
The Black Swordsman from Kigeki will lend his services only if his employer gives him a book upfront as payment. If he happens to like the book, then you've just secured yourself a VampireOne-Man Army.
Yang Wenli, an aspiring historian turned strategist due to various circumstances, of Legend of Galactic Heroes. He has never been defeated in his career, besting even the Empire's brightest star Reinhard von Lohengramm. However, all he ever wants in life is early retirement and a generous pension so that he can pursue his real interest: study history.
Elliot and Oz also count. The both of them spent their first conversation fighting over their favorite characters from their favorite book. The former, while not as good as many others, is still an able swordsman who is not afraid of rushing towards a Chain to save his friend and the latter has control over B-Rabbit's power, especially considering he is B-Rabbit, to begin with.
Black Lagoon's Rock is probably the most dangerous character in the whole series. Not only is does his business and schmoozing experience cause him to be the best negotiator of the Lagoon company he also plans out the events of an arc before hand based on his limited knowledge of the characters involved..
Samurai Deeper Kyo gives us Hishigi, as well as Yukimura and the Sendai Aka no Ou (the latter two spend their entire fight quoting Confucius at each other).
From Digimon Savers, we have Masaru's dad, Professor Suguru Daimon. Brilliant scientist who designed and built the Digivice iC, and considering he did it in the Digital World, he probably had less to work with than Tony Stark's box of scraps. He is also a massive Hot-Blooded badass, who can punch out even the strongest Digimon, fought his partner BanchoLeomon to a standstill with his fists in their first meeting, and saved the Holy Captial by smashing a hole in the ground with his fist, making water burst out. And he actually survives getting a huge hole punched in his chest long enough to transfer his spirit to his partner's body. One of the most badass ass-kicking scientists ever.