The summoner Corona uses her intelligence and controls her strong Golem, Goliath.
A description used for Maka (brains) and Soul (brawn) from Soul Eater, which appeared to be the case only initially. Soul's understanding of insanity and music has given them the upper hand on several occasions, showing that he does take time to think and come to useful (at times life-saving) conclusions. While Maka's attempt at gaining 'strength' through brute force originally got her nowhere (except off of London Bridge), her recent victories have demonstrated her increased physical ability. Tsubaki and Black Star are a better example, where it is the Weapon who is the sensible one, and the meister the brash - but ultimately effective - bruiser.
Goku and Bulma were essentially this early on in Dragon Ball, before it became less about adventure and more about martial arts.
Code Geass has Suzaku who pilots the Lancelot, and Lloyd Asplund who maintains it. Kallen and Rakshawta have a similar relationship concerning the Guren II.
Puella Magi Oriko Magica has the titular Oriko and her (girl)friend Kirika. Oriko is a seer and only fights at the very end of the series. Kirika is batshit insane and rather talented at killing things. Together they cause the plot.
Choji and Shikamaru from Naruto could also count as it is Shikamaru's intelligence and Choji's strength that is the main focus of their attacks especially when they work together.
In Chaotic, Borth-Majar is one creature in regards to the rules of the card game, but consists of two entities: A super-smart midget with no offensive power who rides on the back of a dumb-as-rocks rock monster who is barely able to cast spells on his own. Be sure to practice before using "divide and conquer" tactics with them in the Dromes, though, as trying to be in two places at once can be highly disorienting.
The central characters of Marvel Comics's Incredible Hercules are the titular legendary Greek hero, one of the strongest men to ever walk the Earth, and his teenaged travelling companion, Amadeus Cho, who is inexperienced but incredibly smart; they often work for/with Herc's sister Athena, another genius, though of the Chessmaster type.
Astérix is the Brains and his buddy Obelix is the Brawn.
Luke Cage and Iron Fist are best friends and frequent partners. Fist is the brains, and Cage is the brawn.
X-Men allies-and-sometimes-enemies, the Shi'ar Imperial Guard, has B'nee and C'cill, two symbiotic mechanoids who could have inspired Master Blaster. One is big, clunky, armored, and sub-sentient, the other is small, agile, and has tactical skills. They are apparently named after "Beany and Cecil", a kids' show.
Among the X-Men themselves, one of their more enduring couples is computer geek Kitty Pryde and team powerhouse Colossus.
And their enemies, Juggernaut and Black Tom Cassidy. They're of comparable intelligence, but Black Tom is a plotter and Juggernaut is an enforcer.
Dwight from Sin City is capable of handling himself in a fight but if he can help it, he likes to think his way through problems while his friends kill the bad guys. He often has Miho do all the dirty work but one story did involve him enlisting Marv's help.
Though they're not really a team as such, Dilton Doiley and Moose Mason from Archie Comics get on better than most peripheral characters when they do meet — possibly because Dilton has little real interest in girls (beyond anatomy, and that's not a double entendre), so Moose doesn't have to beat him up for hitting on Midge.
You could likely count Peppermint Patty and Marcie from Peanuts here. Marcie, being a nerdy "book smart" type, would be brains, helping her friend with any intellectual situation. Patty, however, is a tomboyish "street smart" type (brawn) who has to help Marcie any time they're outside of school, defending her (and often anyone else) in any physical confrontation.
Whenever Batman and Superman work together, they respectively serve as this to one another.
Xadhoom and Paperinik does this with a catch: Xadhoom is a Genius Bruiser, but her tendency to be The Berserker means he had to come up with a plan. Paperinik and One form a more traditional pair. There is also a whole planet (Vanium) where each member of the strong but dumb race lives in symbiosis with a member of the weak but smart race.
Chunk and Sloth make a weird sort of comic/heroic pair in The Goonies. Chunk isn't exactly brainy, but he is when compared to Sloth, and he does lead them to the rest of the Goonies. Along the way Sloth demonstrates his incredible strength, for better or worse.
In the film remake of 21 Jump Street, a brains-and-brawn combo help each other get through the police academy (one helps the other learn the law, the other helps the first to pass the physical) and become best buds.
Subverted by Castor Troy and his brother Pollux in Face/Off. At first glance they appear to be the brawn and brains respectively, but Castor is more than capable of cunning, and Pollux has a high IQ, but also an Ambiguous Disorder that causes him to screw up simple things. Furthermore, Castor is the main villain and the one who switches faces with Sean Archer.
Hiccup and Astrid in How to Train Your Dragon. Astrid is very smart, but not like the nerdy and innovative intellectual that Hiccup is. Astrid is the rough-and-tumble warrior who's goal is to become a dragon fighter and Hiccup uses his intellect to train a dragon. Together they get rid of the dragon pest problem and by the end of the movie become boyfriend and girlfriend.
Masterblaster in Mad Max: Beyond Thunderdome. The contract killing that Max accepts from Aunty is to break up this arrangement by killing the brawn, leaving the useful "brain" alive so he can continue to run the methane plant that provides power to Bartertown.
Aunty: Masterblaster. They're a unit. They even share the same name.
The Collector: The little one is called Master. He's the brains. He runs Underworld. The other one is Blaster. He's the muscle. Together they can be very powerful. We want to keep the brain, dump the body.
The eponymous pairing in the novel, Freak the Mighty by Rodman Philbrick: Freak is a short handicapped kid (but brainy), Max (the narrator) is a Gentle Giant that people assume is stupid, and together they are Freak the Mighty.
Inigo isn't really very bright; he's just smarter than Fezzik. Conversely, Fezzik is much stronger than Inigo, but since Inigo is the world's second greatest swordsman, he's quite capable of providing his own brawn. Unless he needs a door broken down.
He wasn't as motivated as the man in black so I'm going with best in the world
They actually go into this in a fair amount of detail in the book: The Man in Black is (barely) better than Inigo in a clear, open field, but he has no idea how to use terrain to his advantage or counter dirty tricks like Inigo does. Inigo is walking all over Wesley at the beginning of the duel, underestimates him, and lets the fight get into the open where Wesley is able to keep Inigo from escaping and wear him down.
...is an aversion. Fafhrd is repeatedly shown as being highly intelligent and intellectually curious (he trapped a socratic scholar with logic) while the Mouser, if you're keeping count, is actually the more dangerous of the two in a fight. Both have personality quirks that occasionally make them do VERY STUPID things (the Mouser keeps getting carried away with his own love for his "cunning" and winds up overreaching himself, while Fafhrd is too fond of embracing his capacity for self-delusion) but both are smart AND tough.
Subverted in that Ivan turns out to not actually be an idiot—just lazy, and willing to use Obfuscating Stupidity to avoid being put in charge of anything, or responsible for anything.
Miles: Do you think of yourself as an innocent bystander? Ivan: God knows I try to be.
The Gentleman Bastard series has a complex relationship with this trope.Small guy Locke Lamora is, for most of the series, partnered with 'muscle and fat' bruiser Jean Tannen. Jean is a merchant's son, and has a very solid academic education, while Locke is a Satisfied Street Rat, but a very quick thinker and cunning planner. However, Jean is quite capable of putting together and executing creative and effective plans, even if they aren't quite as elaborate as Locke's.
Mentioned, in name if not in spirit, in Anne McCaffrey's The Ship Who Sang and its sequels — each "brainship" is assigned a "brawn" who acts as companion, ambassador and muscle for the immobile cyborged pilot encased inside the ship. Averted because brawns are also required to be pretty damn smart in order to come close to the pilot's abilities. As mentioned below, they also serve as someone to say to the other, "why are we heading to [planet / space station / Negative Space Wedgie] again?".
In a 1950s science fiction novel about the first manned spaceship flight to Mars, whose name I have long ago forgotten, the two-man crew is introduced to each by the chief scientist thusly, "Brains, meet Brawn. And Brawn, meet Brains"
Artemis Fowl and (Battle) Butler. Butler is actually pretty smart, but standing next to Artemis (Who, as far as we know, is the smartest person on, or under, the Earth) even he looks dim.
Conan agreed. He generally agreed to her plans. Hers was the mind that directed their raids, his the arm that carried out her ideas.
A Song of Ice and Fire's Bran and Hodor make what is probably the most extreme example on both ends, Bran being a 7-9 year old lordling that gets crippled at the beginning of that first book., Hodor being the gigantic oaf that only knows how to say his name (and it's not even actually his name) that is put to the task of carrying him around wherever he goes.
Tyrion, a genius dwarf, and his sellsword friend/bodyguard Bronn (which even sounds like brawn), though Tyrion has fought in battle twice and Bronn is Street Smart. Subverted when Bronn decides that working with Tyrion has too many risks. Its nothing personal, just that sellswords can't afford to be eternally loyal.
Ciaphas Cain, HERO OF THE IMPERIUM, to some degree. While Cain does kick copious amounts of ass with sheer skill and light weaponry, physically he is no match for Jurgen, a sturdy Valhallan who skips wussy laser pistols in favor of a BFG melta gun. Cain is a Guile Hero while Jurgen is socially stunted, Literal-Minded and largely considered ignorant by most (though Jurgen has a decent case for more being Book Dumb and is very capable in the areas of scrounging and being prepared).
Fisk (brains) and Michael (brawn) from the Knight and Rogue Series. Fisk is actually good with knives, but prefers to stay out of fights, and Michael, who does have some bright moments, actually has more of an education than Fisk, but you'd never notice it.
In Galactic Patrol, the quartermaster deliberately rigs a drawing to pair the captain Kimball Kinnison (brain) with marine sergeant Peter vanBuskirk (brawn).
Lampshaded as the two fight through a hostile jungle:
VanBuskirk: But we're quite a team at that, chief - brains and brawn, huh?
Kinnison: Uh uh. Grace and poise; or, if you want to be really romantic, ham and eggs.
Definitely a case where it's only relative: Kinnison is pretty big and muscular except when you stand him next to a Heavy Worlderspace marine, and vanBuskirk is far from stupid, even if he does have a mental block when it comes to higher mathematics.
Aubrey-Maturin: Jack Aubrey and Stephen Maturin are a subversion that seems played straight at first. Stephen Maturin is a 5'6" tall, ill-looking physician and naturalist, who can never grasp details of life at sea. Jack Aubrey is a 6'6", heavily built naval war hero, whose body is covered with scars from various boarding actions he commanded, and who constantly fails hilariously at quoting The Bible or classical literature. However, Stephen manages to defeat several of Jack's lieutenants at fencing practice, and follows it up with shooting the pips off a playing card at twenty paces. Meanwhile, Jack has very little natural curiosity and sees no value in learning for its own sake, but will hurl himself head first into any academic pursuit he believes to be useful. When the series ends he has been one of three RN captains chosen for their astronomical skills to observe the passage of Venus (a once in a millennium occurence), his papers on geometry have won him a Fellowship in the Royal Society, and he always builds all his own telescopes and spyglasses.
There's a minor example - they're human kids who're thirteen and twelve respectively - in Tash and Zak Arranda in Galaxy of Fear. Tash is a bookworm and more thoughtful and insightful, and also gradually develops her skills with the Force. Zak is twelve but stronger, and is more direct and physical as well as being Book Dumb. By the end of the series, Zak is aware that Tash's skills have just become more useful than his - next to her telekinesis and their uncle being a scientist and a Shape Shifter, he doesn't feel like much.
Rehaek and Torath in the Star Trek Novel Verse; the one-time head of the Tal Shiar and his bodyguard/lieutenant.
Once Frank and Joe Hardy were allowed to have personalities, they frequently got compared this way. Frank was taller, leaner and more calm and logical. Joe was shorter, more muscular, and prone to being impulsive and hot-headed. Only a partial example as they're both shown as very tough and very clever, they just finally started to complement each other's personalities better.
Merlin: Merlin (brains) and Arthur (brawn). Merlin is sort of defaulted into the position of brains because (unlike Arthur) he usually knows what's actually going on. Amusingly, Arthur seems to consider himself the brains and the brawn of their two man band and takes delight in calling Merlin an idiot, useless buffoon, girl's petticoat, etc. — although, if you don't know that Merlin has magic, his antics do seem a bit strange. Although in the later episodes, Arthur seems to be realizing how clever/talented Merlin is, but is extra mean to hide his fondness of his servant.
In fact, as far as the magical side of the series goes, Gaius is the brains and Merlin is the brawn — Gaius knows everything there is to know about everything but doesn't like to use magic, while Merlin, the most powerful warlock of all time, manages to consistently not know anything about the evil magic of the episode until Gaius does the research for him. Granted, Gaius is his mentor, so it's sort of in the job description.
Finch and Reese respectively in Person of Interest. Reese is more of a Genius Bruiser, however, especially compared with Finch's first partner, who was more brawn and a lot less brain than Reese.
In Big Wolf on Campus, Tommy Dawkins is the school's quaterback in addition to being a supernaturally strong and fast werewolf. His best friend is Goth nerd Merton J. Dingle, whom Tommy sought specifically because he believed Merton was the only guy weird enough to know what to do about his new wolfy condition. When its time to fight the Monsterofthe Week, Tommy will do the fight part while Merton will inform him of the monster weaknesses.
Prison Break's protagonists are Lincoln Burrows, a street tough framed for murder, and his brother Michael Scofield, an engineer with a genius escape plan. The "brains/brawn" comparison is made several times.
"With my brains and your brawn, we'll make an excellent team!"
The above quote from Half-Life is one of the lines you'll hear when the hero, Gordon Freeman, enlists a scientist to help him out during a stage. It's also something of a parody, given that the "brawn" is a nuclear physicist.
Somewhat inverted in Half-Life 2 when Gordon is teamed up with Action Girl Alyx Vance for some of the game and practically all of Episode 1 and most of Episode 2.
As for Metal Gear Solid: Peace Walker for the PSP, usually the combat-team are considered TheBigGuys, who leave Mother Base to complete various fighting/sneaking missions. Meanwhile, the R&D team, Intel team, Mess-Hall team, and First-Aid team are usually considered TheSmartGuys, in that they stay behind at Mother Base to provide food, medicine, equipment, and information for the combat-team.
Uncharted: Drake's Fortune has the brawn/brain team of Nathan Drake and Victor "Goddamn/Sully" Sullivan, if only because Sully acts as a father-figure to Nathan Drake, always providing words of wisdom to help Drake survive each adventure, while Drake protects Sully with his muscles and guns.
Max and Da Silva in Max Payne 3. Without Da Silva, Max Max would have long lost the trail, making his gunfighting skills little use, and as Da Silva notes, without Max to act as an iron fist, he would at best be ineffectual and at worst made an example of.
Elizabeth and Booker in Bioshock Infinite as Elizabeth spent the majority of her life reading while Booker spent alot of his life killing.
In Borderlands 2's "Captain Scarlett and her Pirate's Booty" campaign, one of the main villains is Scarlett's arch-rival Sandman. When you finally meet Sandman, it turns out he's a midget with a massive bodyguard called the Big Sleep. Sandman's Boss Subtitles note that he's "totally the brains of the operation."
In Awesomenauts, the characters Vinnie and Spike are a classic criminal pair, with Vinnie as the brainy gangster and Spike as the dumb muscle. In game, Spike technically is the one you play as while Vinnie rides on his back and does all the talking, see?
Star Fox respectively has Slippy Toad and Peppy Hare.
When the cast of Dubious Company gets stranded on the Island of Nowhere, Izor divides everyone into this. The Brains are to figure out a way home, while the Brawn gathers resources and sets up camp. Hilariously:
T-Bone and Razor in SWAT Kats are something of a subversion: Razor invents all the gadgets and weapons, but he's a martial arts expert and arguably the better fighter of the pair, while T-Bone is a Boisterous Bruiser who's also an excellent mechanic and genius pilot.
Robin and Superboy are often teamed up this way in Young Justice, though Robin is still good in a fight and Superboy is still plenty intelligent. The best example would be their take down of Batman and Superman in the finale, where Superboy throws Robin hard enough that he knocks Batman into a wall and stuns him, then pulls out the Kryptonite to stun Superman while Superboy has him in a hold.
Usually, at an average house-hold, The Big Guy is usually the breadwinner, going out of the house to work to earn paychecks needed to purchase vital goods for the house. Meanwhile, The Smart Guy is usually the homemaker, staying at home to utilize the vital goods to take care of the house, so that The Big Guy could rest and recuperate from a long day at work or outside the house.
Anime and Manga
Sora and his twin brother, Nike, in Air Gear are the two official leaders of Genesis. Sora being the brains behind all of Genesis' operations and Nike being the brawn that goes out and does the more physical work. Before Genesis though, it seemed that they were more Bash Brothers.
For his final form in Digimon Frontier, Lucemon becomes two seperate entities; a powerful and gigantic dragon that is no more intelligent than an animal, and a smart and relatively small insect that resides within a sphere carried and protected by the dragon.
Another Neil Gaiman example from The Sandman. Brute and Glob, two 'Major Arcana' (the most powerful and significant of dreams)that go rogue during his imprisonment. Exploiting Dream's law against killing mortals, they manage to create a barrier inside the mind of an abused child even Morpheus can't easily penetrate.
Tz'how and his wife Jessica in Bowling King. Tz'how is a bowler with powerful arms, but he thinks it's an astonishing coincidence that Michael Jackson and Janet Jackson resemble one another and has a pretty advanced case of amnesia. Jessica, meanwhile, uses his lacking intelligence to keep him from regaining his memories of their past together and constantly plots to live comfortably with him.
Early in Daredevil comics, Mr. Fear specifically hires the Ox and the Eel as his enforcers because they're, respectively, incredibly powerful but too slow to challenge his leadership and cunning but lacking the strength to oppose him.
According to Anne in S.S.D.D, Richard and Norman used to be "like those guys from Mad Max".
Tulip and Pin from the Discworld novel, The Truth.
Terry Pratchett, writer of said novel, has had fans point out to him that it's "obvious" that Tulip and Pin are based on Croup and Vandemar, and had this to say:
"Fiction and movies are full of pairs of bad guys that pretty much equate to Pin and Tulip. They go back a long way. That's why I used 'em, and probably why Neil did too. You can have a trio of bad guys (who fill roles that can be abbreviated to 'the big thick one, the little scrawny one and The Boss') but the dynamic is different. With two guys, one can always explain the plot to the other..."
Heroes had the firestarter siblings, of whom the stronger brother was told by his father that God gave him a sister instead of a brain. The sister wasn't all that bright either.
Topher and Dominic have tension between them as two of the bad guys running the "Dollhouse." Dominic, a bodyguard, regularly uses threats of physical violence on Topher to ensure he's doing his job well. Topher, a programmer, regularly uses witty barbs on Dominic to rub it in that he's smarter.
The first one is Queen Valentina (brains, seeing as she's the Evil Genius attempting to usurp the throne of Nimbus Land) and Dodo (brawn, as he's her Dumb Muscle bodyguard). This is also true as far as gameplay is concerned; during the Boss Battle, Valentina has powerful magical attacks, but is rather weak physically, while Dodo (brawn) has powerful physical attacks.
Cloaker and Domino is the second pair. Domino (brains) has powerful magical attacks, but cannot use or withstand physical attacks, while Cloaker (brawn) has powerful physical attacks, but cannot use or withstand magical attacks.
There's also Wario and Waluigi. The latter is the brains while the former is the brawn.
Minerelle and Joey try to be this during a Something Awful: Dungeons & Dragons Paragon Tier session, conducting a hilariously terrible investigation of the town they're in while trying to sniff out a shape shifter. They aren't very good at it, due to a combination of some terrible dice rolls and neither of them being particularly smart.
Rocky and Mugsy, from a series of Bugs Bunny shorts.
Ransack and Crumplezone from Transformers: Cybertron. In a slight subversion, Ransack often comes across as not especially bright either, and being the brains only because Crumplezone is several times thicker than a titanium-reinforced brick.
Really villainous? They're more like anti-heroes, because their principle is not to do evil. Besides, Ren is very much both brains and brawn, taking his occassional Unstoppable Rage into account. Stimpy is, it would appear, neither.