Also, Joshua. He's the most intelligent member of the playable cast, and he's the Composer, which means he's a physical god.
The Half-Life series revolves around an interdimensional war between alien empires that spills over to an alien invasion and conquest of Earth, in which the human fight against the alien invaders is almost entirely in the hand of theoretical physicists.
Most famous the main protagonist Dr. Gordon Freeman, who only gets to show off his scientific expertise by performing the tasks of a lowly lab technician, but according to the manual, he just returned to America from his last university job in Europe and got his now employment in probably one of the worlds biggest and most secret research facilities. On the badass side, he kills hundreds of alien soldiers and monsters in the span of three days and travels to an alien dimension to kill an Eldritch Abomination with machine guns, laser rifles, and rocket launchers.
And then there is also the staff at the Lambda Complex, who have been doing expeditions into the hostile alien dimension for quite some time.
In Half-Life 2, the human resistance against the alien occupation is apparently founded and lead by the leader of Gordon's old team, Dr. Eli Vance. The rest of the inner circle include Dr. Kleiner, Dr. Mossman, and Dr. Magnusson. While neither of them are great fighters, they still have been leading the fight against an alien empire for well over a decade.
Alyx Vance, the daughter of Dr. Eli Vance, seems to be the resistance's main muscle and top infiltrator. Since there haven't been any universities on earth since she was a little girl, she does not have a degree, but she's still one of the world's experts in dimensional travel and teleportation. And also an expert electrical engineer.
And while certainly not a badass in any sense, even the human puppet governor of Earth, Dr. Wallace Breen, the former director of the Black Mesa Research Facility, is a physicist.
Lexicus Runewright in RuneScape. Looks like a harmless librarian before he starts summoning books that shoots pages at you, plus multiple exploding books that could easily tear you to shreds if you don't have the sense to run.
Probably one of the earliest FPS examples is The Hacker from System Shock, where he manages to survive in the space station filled to the brim with mutants and cyborgs controlled by the Megalomaniac AI. That Military-Grade Neural Interface probably helped too.
Extremely literal video game example: Lex (a worm) defeats a variety of monsters and creatures of legend in Bookworm Adventures, despite the fact that he is lacking not only weapons but limbs. And he is also using the power of words.
Several of the magic users in Fire Emblem, especially if they're of the Mage/Sage, Cleric/Priest/Bishop or the Shaman/Druid classes. More specific examples are:
Then there's The Protagonist, who is not only the most powerful and versatile fighter in the entire game, but is also a genius who can consistantly rank as N.1 in his school level (assuming that you take the time to level up his Academics stat).
Daniel Dankovski from Pathologic is a world-famous pathophysiologist, but he is also an excellent sniper and sharpshooter, and he is very strong at knife- and fist- fight.
Nightwolf from Mortal Kombat, before Hell broke loose in MK3, was a historian whose knowledge of both shamanism and Native American legends as well as his physical strength was what made him qualified to become one of the Earth Warriors. In the cartoon, he's also a computer genius on top of a fighter and a walking myth encyclopaedia. In the original arcade Mortal Kombat 3, as Nightwolf, you could actually throw your opponent, run after him, and throw him before he had a chance to recover. Also, in the newer games, he tends to have easy combos that take 25% of your life bar.
Citan from Xenogears is one of the best examples of this. He enjoys reading, tinkering with machinery, and other bookish hobbies, yet is one of the planet's best swordsmen, as well as being a master Gear pilot who has had an Omnigear since even before the events of the game).
The first six members of Organization XIII have this as part of their backstory (or so we assume); Six brilliant apprentices of a wise and loved king... who manage to release The Heartless on the worlds and become the most powerful Nobodies around. Zexion, who was one of the original 6 Organization XIII members, fits this trope. His weapon? A book.
Hugh from the second installment is seemingly just some random biologist who can use status debuffs, nothing especially useful, until he gains a surprisingly accurate multi-target insta-kill spell. That and the fact he can use a mace!
Hahn from the fourth game also does this, but can combine it with something else to cast Holocaust (you have to be badass to get away with that level of tactlessness)
Jaina Proudmoore in Warcraft III is actually like this, seeing that she really LIKES studying and declares to be 'in love' with her studies or profession as a mage, since it lets her study a lot.
Patchouli Knowledge from the Touhou series is a pretty good example of the "magician" variety: she closets herself in (what amounts to) her own private library virtually all the time — researching new and innovative ways to produce More Dakka. And she's not afraid to use them! Though the badassness level is sometimes slightly hurt by the fact that her frail health and asthma, due to lack of exercise and open air, can impede her ability to recite the incantations or endure protracted battles. Not that most people live to see the point where this matters.
Nitori Kawashiro. She goes by with the nickname "Super Youkai Warhead", and arms herself with an Extending Arm plus and Invisibility Module she built herself, despite the fact that the general level of technology in Gensokyo being equivalent to the Sengoku Jidai era. Or even earlier.
Keats in Folklore goes from mild mannered skeptical Intrepid Reporter to destroyer of souls with seemingly little convincing.
Chrono Trigger's Lucca. She built a robot and a teleporter while living in a quasi-medieval time period, and the Time Key you use through most of the game. Her techo-geekness is established by her house, strewn as it is with books and cabling. She later repairs a robot 1,500 years ahead of her time. She also wields pistols and fire magic.
In older versions of Dwarf Fortress, order your bookkeeper to take the most accurate inventory of your stocks possible. He, a weak, unassuming social dwarf, will proceed to lock himself in his study, and work silently for roughly a season. Eventually, he will re-emerge, and after all those hours of updating the records, will have acquired the character notes 'Ultra-Mighty', 'Extremely Agile', and 'Unbelievably Tough'.
Shad, from The Legend of Zelda: Twilight Princess, could be a contender for this trope. He's a textbook nerd, with glasses and argyle socks and a freakishly large bow tie, who natters on extensively about the ancient race of bird-people called the Oocca. He's also tolerably muscular, uses an ornamental dagger as a bookmark, and forms a Resistance with the characters Auru, Ashei, and Rusl — all of whom are easily defined as being badass. Plus the ancient Hyrulean BAZOOKA. It stands to reason that Shad wouldn't be part of that little collective if he couldn't hold his own.
Lucian of the Elite Four in Pokémon Diamond and Pearl mentions that he just finished a book when you arrived and has the book depicted in his entering battle animation in Platinum. He's the last of the Elite Four, a devastating Psychic-type specialist. If you talk to him after beating him, he mentions he's going to go back to reading in order to prepare for his next battle. Awesome. You can run into him at the Canalave Library once after having entered the Hall of Fame your first time.
On a similar note, Shauntal, the Elite Four's Ghost type specialist in Pokemon Blackand White. She's a lot like Lucian, except that she writes books as well as reading them.
Pokémon Ruby and Sapphire: Rustboro Gym Leader Roxanne is also depicted as one, especially in the manga - where she forces all hopefuls into taking a written exam for the right to challenge her. It's pretty verbose on top of that, meaning that with one exception, everyone who got to fight her had some serious language comprehension skills.
Cyrus from Team Galactic. Scientist, engineer, roboticist, strongest Pokemon trainer in the team and one of the strongest trainers in all Sinnoh, and the man who captured the embodiments of Willpower, Emotion, Knowledge, Space, and Time.
Uxie and Azelf could be this in Pokémon form. They're small, Psychic-type pixies, so it seems like they would specialize in the Special end of the spectrum, which is partially true; Azelf's Special Attack is very high. However, its physical Attack stat is just as high. Uxie's got better defense and special defense stats, but it being the Knowledge Pokémon qualifies it as this trope. Mesprit is in-between.
Blazblue has Litchi Faye-Ling, a former scientist of Sector Seven whose seithr theories and experiments is widely acclaimed and praised by many, including even the likes of ReliusClover. Aside from this, she is also a competent fighter, and with the power of Lao Jiu siphoning the Boundary's power for her, she is able use a staff which she can manipulate with her mind, as well as magical-based attacks.
Edmund from Gaia Online got his start as a Mad Scientist. Then he became a superhero. Then he fought off an Ax-Crazy vampire hitman... multiple times... These days, he's supposedly retired. Supposedly.
In the prequels, we have Emmy Altava, who can almost keep up with the professor in terms of puzzle solving ability and can beat up goons far larger than her.
Final Fantasy Tactics: the Calculator does stuff with math. Stuff like injuring every enemy on the screen. At once. Since the game lets you change classes, every one of your characters can learn to be a bookworm. Combine this with all the other classes... Badassery out the behind.
An evil variant is Balk, a disgruntled machinist who aids the Corrupt Church in their proletarian killing spree. He always comes packing some horrible magic-shooting gun, and likes to snipe at you from an advantageous position. If you want a warrior's job done right, it sometimes takes a scientist.
Nu Mou Scholars in Final Fantasy Tactics A2 use books as their weapons of choice. Seriously, no one expect a short and fragile race like the Nu Mou to be physically strong since they specialize in magic, but Scholars can deal a good amount of physical damage and use spells that hits everyone by just reading from the book. Human Seers also uses books for weapons and their Magick Frenzy ability lets them hit enemies with spells AND the book.
Not only can Calculators nuke every enemy on the screen with high-level spells, they do it for no MP cost! If properly used, Calculators are an even bigger Game Breaker than the infamously broken optional character Orlandu.
John Vattic from Second Sight, a skinny, awkward-looking academic... that also happens to be one of the most powerful psychics in the game. Plus, as seen in the first level of the game, he can kill people with his bare hands.
Briar Rose in The Lost Chapters expansion of Fable I. Spends a lot of her time shuttling back to the Heroes' Guild to research eldritch incantations and ancient prophecies, but is fully capable of throwing down on fell abominations when necessary.
In Mass Effect, due to the highly advanced technology of the setting, most people are either this or a Genius Bruiser. Any class reliant upon tech attacks is usually this, as are a few biotics.
Tali'Zorah nar Rayya: don't let that 'all tech' rating fool you, she can pack a mean shotgun and gets the strongest shields in the game by default, in addition to her ability to kill you with her toolkit. Quarians in general tend to fit the trope. Their entire life and culture revolves around spaceships and technology, and their environmental suits make them look like skinny engineering nerds. But don't let that fool you.
Professor Mordin Solus. Motor Mouth doctor. Ran clinic during plague, threat to mercenaries. Came to start trouble. Killed them, left bodies on display. Formerly part of Special Tasks Group. (inhale) Never saw him coming. Salarians in general fit trope. First impressions awkward, but Salarian ingenuity, intelligence, and logic will hold the line.
To a degree, Kaidan Alenko. He's a techie with medical training who initially appears to simply be a Nice Guy. However, as you learn later, he's also an incredibly powerful biotic (for a human) who (accidentally) killed one of his instructors in biotic training who threatened the girl he liked and then Kaidan after Kaidan stood up for her.
Sentinel Shepard, having learnt to combine biotic abilities and engineering on the battlefield to devestating effect, in addition to their N7 special forces training. How badass is Sentinel Shepard? It's possible to complete the game on Insanity without firing a single shot. Shepard doesn't need guns. Engineer Shepard also qualifies, even getting a bonus to research due to their intelligence.
Kasumi Goto is a master thief turned Cerberus affiliate/asset, however briefly. Once she's been recruited, paying a visit to the observation deck she's claimed as her personal quarters reveals that she enjoys various forms of artistic expression, literature included. Especially noteworthy since this is a future where all those books would be available electronically through the extranet for a much lower cost, except she simply enjoys holding an actual book while reading. Besides, being a master thief probably helps circumvent the cost issue. She also writes haiku. About Jacob's dreamy abs.
Alexandra Roivas is a student in abstract mathematics and number theory.
Her grandfather was a clinical psychologist who, in the chapter you play him, gets two of the most awesome guns in the game (a sawed-off shotgun that can be used at close range to remove one arm and two heads from 9-foot-tall brutes, and an elephant gun that knocks him over when he fires it). Other people were Edwin Lindsay (Think Indiana Jones, with a beard), a 14th-century monk, Roberto (an architect during the Renaissance), and a WWI journalist who puts all that spare ammo lying around to good use. Everyone gets to dismember zombies and other monsters.
Tails from Sonic the Hedgehog. He is a freaking genius, even making a robotic suit that rivals Eggman's, while at the same time being fairly fast, having the ability to fly, and, in some games, being able to take out Eggman by himself. Not through intelligence, though. No, through beating the ever loving crap out of him! In Sonic Adventure, he has to go and beat Eggman to a missile then take on one of Eggman's mechs by himself, saving the city SINGLE HANDEDLY.
Alex Mercer from [PROTOTYPE]. Before the events of the game, he had already earned a PhD in genetic engineering by age 29, and it's heavily implied that his work was leaps and bounds ahead of everyone else's. Then he's infected with The Virus and offensive abilities so great that he can slice a tank in half (and then pick up those halves and smash helicopters out of the sky with them) and decimate entire bases single-handedly, as well as defensive abilities that enable him to survive point-blank tank fire and survive a direct hit to the face with a nuke. Oh, and he also gains all of the knowledge and memories of anyone he consumes — yes, that includes other geniuses, as well as military personnel whose expertise lies in operating tanks, choppers, etc.
If leading the Squad that wins practically every major victory of a war counts as badassery, Gunter Welkin from Valkyria Chronicles definitely counts. He's not a true soldier but just a student learning biology to become a school teacher. A skill which actually helps him win a number of critical battles, by using the environment to his advantage.
Trilby, from the Chzo Mythos, studied hard at engineering and mechanics before turning to the life of a Gentleman Thief. What truly makes him a badass is that he used his skills to face the forces of evil not once, not twice... but THREE TIMES! Having also become a Man In Black he becomes the stuff of legend.
Mical/Disciple and Bao-Dur from the second Knights of the Old Republic. Mical is a historian and spy trying to salvage Jedi history and lore for the Republic. You meet him doing a little "light" reading in the bombed-out, nasty-critter-infested ruins of the Dantooine Enclave. His starting class is Soldier (VERY tough, plenty of combat feats), but you cross-class him to a Consular (MASSIVE amounts of Force whoop-ass). Bao-Dur is a shy, soft-spoken engineer who came up with such a nasty weapon of mass destruction (the Mass Shadow Generator) that even the Mandalorians were horrified when they saw it in action. He's also no stranger to more...personal combat, either. It's what cost him his left arm. Badass he is, he built his own artificial one. You can cross class him as a Guardian (mostly because his mechanical arm prevents him from wearing robes, thus limiting his ability to use Force powers anyway).
Tales of the Abyss has Colonel Badass Jade Curtiss. He discovered/invented fomicry, a branch of science, by himself before he even turned ten; he is the personal confidant and right-hand-man to Emperor Peony, with some people speculating that Jade is really running things through his emperor; he is well versed in several scientific subjects, including medicine; he figures out the game's big plot twist almost instantly, if you pay attention near the beginning of the game; he is, excepting seventh fonists, the most powerful fonist in the world; by the end of the game he's even shrugged off the effects of a Fon Slot Seal, a rare and dangerous weapon akin to a nuke in-universe.
In Tales of Symphonia, Genis is small, he's smart and carries a toy kendama as a weapon. He also has the most dangerous spells at his disposal. His sister also has her moments.
In Tales of Vesperia Rita Mordio qualifies as well, she is a dedicated blastia researcher not older than 15 who can also burn their enemies to a crisp.
She's quite agressive too.
Super Robot Wars has Shu Shirakawa, pilot of the Granzon. He has multiple P.H.D.'s at age 21, a strong grasp on alchemy, and improved on technology granted by Guest, which involves weaponized black holes. Also, he and Jade Curtiss above have the same seiyuu.
Jason Hudson, the secondary protagonist of Call of Duty: Black Ops; in addition to being a double-major in psychology and political science prior to his service, he is described as an excellent tactician with genius-level IQ.
In Heroes of Might and Magic V Tribes of the East, vampire lord Giovanni dismisses Arantir as a humble bookworm, then attempts to backstab him... and Arantir easily eradicates him. Arantir points out that there is great power to be found in books, especially magical ones.
Father Elijah, the Big Bad of the Dead Money DLC, braved the wasteland, the Divide, the Big Empty, and the Sierra Madre with his trusty Gauss Rifle and various jury-rigged technology, despite being in his seventies. He's also a genius; he managed to modify various Lightning Guns to be even more deadly, outsmarted all the assassins sent after him, hacked the Think Tank's robots (the ones he didn't kill, anyway), and outsmarted the Think Tank themselves, the "gods of the Big Empty" according to Ulysses.
Shantotto from the MMO Final Fantasy XI easily qualifies. She's short, a professor, and can cast ancient magic spells without using what some would call the "magic casting pose."
She also says everything in a rhyme, for most people that would take a lot of time.
Edgar Roni Figaro from Final Fantasy VI is an engineer who outfitted the entire Figaro Castle with the ultimate defense—a submerge mode! He also fights with his engineering tools, including a drill, a bolt gun, and a CHAINSAW. And he's the king.
Mia, a soft-spokenprofessional medic with students of her own at an Improbable Age, sets out to stop the incursion at Mercury Lighthouse as soon as it happens. When that fails, she forces her way into Isaac's group to track down and stop the villains for good, and in The Lost Age is such a force to be reckoned with that Agatio is (rightfully) afraid of her.
Kraden isn't an Adept... but that makes the fact that he accompanies Felix and Matthew on their respective quests to save the world (and walk across a war zone to join Matthew's!) even more impressive, since he really is just a fragile old geezer with encyclopedic (largely theoretical) knowledge on Alchemy, geography, and mythology, and an easygoing, sociable personality.
Ghostbusters: The Video Game upgrades Winston to the badass bookworm status of his colleagues, stating that he's just received his doctorate.
Shulk in Xenoblade is a rare example of a main JRPG protagonist being this. He is a weapons researcher who is studying the Sword of Plot Advancement, and eventually wields it himself. Even before that, he's pretty adept at swordplay, while being a whole lot sharper than the typical Idiot Hero.
Mages in general in Dark Souls naturally enough. Of the specific NPCs are Big Hat Logan and his apprentice, Griggs.
Pre-augmentation, Adam Jensen of Deus Ex: Human Revolution was a security specialist with ex-SWAT training and an associate degree in Criminal Justice. Post-augmentation, he picked up an interest in clock-making and his apartment is strewn with books on the subject, as well as various others on history, psychology, criminal law and cybernetics. He is also a largely-robotic infiltration expert who can kill you quickly, quietly and in thirty different ways.
Tycho Brahe from Penny Arcade's "On the Rain Slick Precipice of Darkness". Tycho is a scholar who comes from a long family tradition of seeking to end the world and he constantly has his nose in a book. He will throw his book into the air long enough to frag someone with a Tommy Gun, catch the book and continue reading though. His special attack includes throwing the book at foes and later on he 'upgrades' his weapon by mounting the book on it. Yeah, I think he counts...
Chris McShell, Runner 10 from Zombies, Run!, is a quiet, unassuming statistician who is certainly physically fit but doesn't come across as rugged. His kill count is three times that of any other runner. His secret? Analysing the zombie's behaviours over many, many hours of study and theorizing until he came up with a mathematical model for zombie "flocking" behavior, and then using that model to predict their reactions and become a zombie killing machine. He's noted in the Runner's Guide as a "BAMF Statistician". Yes, yes he is.
Guild Wars 2: While the Durmand Priory primarily focuses on the research and reclamation of history, science, magic and technology; they are still expected to be competent, if not exceptionally skilled, fighters, if for no other reason than to combat the dangers associated with such field work. For this reason, their ranks include Guardians, Warriors and even Thieves, in addition to the other "scholar" professions.
Resident Evil: Leon S. Kennedy is described by Ada Wong in Resident Evil 4's Ada's Reports as such: "Practically a genius, he has smarts and knows how to use them." Furthermore, he's shown in the "Leon vs. Chris" cutscene in Resident Evil 6 as being able to fight Chris Redfield himself to a stalemate.
The Elder Scrolls V: Skyrim has Urag gro-Shub, Librarian of the College of Winterhold. If the unusual name wasn't enough of a clue, Urag is an orc. Yes, the big, normally brutish and often rather unintelligent green-skinned type. Urag, however, is a competent mage and will not hesitate to punish anyone who would damage the meticulously-organized and painstakingly-collected contents of his Arcanaeum. He is stern, but otherwise entirely reasonable. Displays some additional Hidden Depths in that he's also one of the few people capable of translating Arch-Mage Shalidor's writings and the Ancient Falmer tomes.
Urag gro-Shub:"You are now in the Arcanaeum, of which I am in charge. It might as well be my own little plane of Oblivion. Disrupt my Arcanaeum, and I will have you torn apart by angry Atronachs. Now, do you require assistance?"
Marc Hawk in Mahjongg Artifacts, an archaeologist who focuses on ancient China and studies martial arts in his spare time. The in-game comic depicts him as well-versed in old legends yet also perfectly capable of beating up some mooks who let themselves into his hotel room later on. Not to mention that near the end of the game he takes on Eldritch Abominations from Atlantis and escapes unscathed.
In Cataclysm this is demanded of the player. As in real life, reading books is the most efficient way to learn new skills and research new crafting recipes. Most players' early-game strategy is to raid the nearest library and spend the next few in-game days reading all the textbooks.
Caira of Evolve. She has multiple master's degrees, was the youngest team leader of Catalog, and wields a napalm grenade launcher against giant flesh eating monsters. And then once she kills them, she cuts them open and studies them.
Taken a step further with Kala. Mentioned as being much smarter than Caira, she has a doctorate in Applied Quantum Molecular Biology, won several accolades in the same field, and fights monsters as a member of The Crew.
In Tropico, it's possible for the Intellectuals faction to take up arms and attempt to overthrow your regime just as any other faction. You can also become this if you pick "War Hero" or "Professor" as your background and "Scholarly" or "Athletic" as your respective trait.
Sans from Undertale, despite being a Lazy Bum is implied to have been of scientific background. There's a book on quantum physics in his house, and some weird machine that he's been working on, not to mention that he seems to have worked with the previous royal scientist. The badass part comes from the fact that he's working as a sentry despite his scientific background... though he spends most of his time slacking off. But if you want to see how badass he really is, go ahead and push his button one time too many. Just remember, you're going to have a bad time.