The majority of the namesake giants from Attack on Titan fall into this category; being slow, lumbering brutes with little to no apparent intelligence that seem motivated by little more than an intrinsic desire to devour humans. The small minority who can actually think and use tactics are actually humans with Titan forms, and one such Titan-shifter is more dangerous than an entire swarm of ordinary Titans.
It's repeatedly implied that this is the case for Marechiyo Omaeda in Bleach, being that he's a gigantically large and intimidating Upper-Class Twit and all... but this is actually just a ruse; He's the lieutenant of the second squad for a reason.
While he may be hiding his skills and intelligence, the fact remains that even when he does reveal them he's still something of a goof, but not as useless.
Played very straight with the 10th Espada, Yammy, who's thick as a brick but tends to instantly kill people with his tree-trunk thick arms. Unfortunately for Yammy, everyone he's done this to has been on his side. Even when he reveals his ultimate power as the strongest of the Espada, his method of fighting is so predictable it ends up boring Kenpachi.
"Little Cho" from Domu: A Child's Dream is slow mentally but also enormous and protective.
Nappa and Recoome from Dragon Ball Z. Nappa isn't that smart (choosing to solve every problem with violence) and follows Vegeta's every order.
Damuramu from Dragon Half is an even bigger moron than any of the other villains in the series. Despite having a somewhat impressive vocabulary and a flair for the dramatic... well, to put it in his own words, "Damuramu's brain is very compact!" This is how he survived being impaled through the head with his own sword. He later resurfaced as an even more powerful cyborg, with such devastating moves as "Damuramu Punch", which is clearly actually a kick.
Durarara!!'s Shizuo Heiwajima, while not as dumb as some examples, is quite simple-minded, easily distracted and forgetful. Shinra jokes that all the calcium that ought to go to his nervous system instead went to his bones.
Ironically, it's this very trait that prevents him from being a pawn in Izaya's schemes. Shizuo is so simple-minded that he becomes unpredictable, making him a potential Spanner in the Works for Izaya's plans at any time. Plus, he hates Izaya (and has ever since they first met), so much so that he flies into an Unstoppable Rage every time he sets his eyes on him, which means he is immune to Izaya's manipulations. It's because of this that Izaya hates him so much.
Otawara is extremely stupid and extremely strong (and incredibly fast for someone his size). He's the only one of the White Knights who's never missed practice, because of a saying about idiots never getting colds. He's also barely literate. Shin (who can actually bench press more than Otawara at the beginning of the series) isn't exactly dumb, but he's so clueless about technology that he broke a GPS by trying to open it because he thought it was a map. This has since become a running gag, where Shin breaks all new technology he comes across.
Homer of the NASA Aliens, as well. He's explicitly described as possessing "stupid strength".
Gaoh was assumed to be this by other players, what with him being only able to wreck the enemy line. However, Hiruma and Kid easily figured out that he's much smarter than he looks, since he knows when to stop being a dinosaur and play by the rules. (ie. whenever the quarterback he's trying to kill makes a pass, thus making it illegal to trounce him.)
Aki "Achilles" Reisuke and Hara "Hercules" Kureji of the Teikoku Alexanders both possess physical prowess befitting their nicknames, but are comparatively lacking in mental faculties (though they're both noted as smarter than total idiot Taki).
Fairy Tail loves this trope. Elfman believes that everything should be settled by fists. With all his manly talk, he still cares for the guild members and his sister; Mirajane. Gray when he unconsciously takes off his shirt. Which half of the members seem to be turned off by this.
Subverted in Fullmetal Alchemist with Alex Luis Armstrong and Sig Curtis. Armstrong acts foolishly carefree, but he is smart enough to fool intelligent characters like Ed or Mustang. Not to mention that his skill at alchemy requires him to be quite intelligent. And when Sig talks is usually to say something important. Between the two, they have more muscles than the rest of the cast together.
Tetsugyuu in the Giant Robo OAV, who is explicitly identified as much more immature and childish than the 11-year old Daisaku Kusama.
Tsuchiya from Holyland is a subversion. Initially he looks like a simple-minded wrestler, but chapter 84 reveals that he can think rather profoundly. Not super-intelligent enough to be a true Genius Bruiser though.
Okuyasu Nijimura from Part 4 of Jojos Bizarre Adventure has the power to erase anything with a swipe of his Stand's hand. If anyone else had this power, they would be able to end fights with a single move, but Okuyasu just uses it to teleport himself closer to the enemy, being too moronic to understand its numerous applications. He's even well-aware of his mental disadvantages: he attaches himself to people like Josuke or his own elder brother (so that someone else can do the thinking for him), and his Catch Phrase consists of variations on "Shut up! I ain't that smart, you know?!?"
The title character of Kinnikuman and his son, star of Kinnikuman Nisei. "Kinniku" means "muscle", and let's just say the big guy's not exactly firing on all cyllinders. This is the most consistent source of humor in both series.
Getatsu/Gedatz. One of Enel's of the 4 priests, Gedatsu is an extremely imposing figure. But he doesn't know how to cross his arms properly, his intimidating Monochromatic Eyes are the result of him rolling his eyes into the back of his head, he attacks his own allies by mistake, and has absolutely zero focus. His fearsome Jet Punch can destroy you utterly with only one hit... if he remembers who you are long enough to try it on you.
Mr. 4, too dumb to think on his own, but can wield a 4 ton bat like it was a normal one.
Oz/Oars/Odz was four times larger than normal giants, he's the strongest zombie in Moria's crew and it took all eight Straw Hats plus Brook (who wasn't their crewmate at that time, yet) to take him down. However, since it's Luffy's shadow for resurrecting him, he was as dumb as him.
Gekidrago from Futari wa Pretty Cure is the first Dumb Muscle and probably the dumbest villain in the whole franchise. Beside a few creative usage of Zakennas, he gives Mepple back to the heroines, who has one of the Prism Stones in his body, when they tells Gekidrago that he's sick. Because he thinks he would get trouble by his boss if he brings a sick mascot back. Of course, after Mepple is cured, the girls kick Gekidrago's ass.
Uraganos from FutariWaPrettyCureMaxHeart tends to not listen to other people and he breaks stuff without thinking. And when he listens to the annoying vice-principal of the heroines' school, he briefly agrees with him, despite actually trying to assault the Pretty Cures.
Dorodoron from Futari Wa Pretty Cure Splash Star is a Shrinking Violet and needs the help of the Kiryuu sisters who make all of his plans. And during his first final battle against the Pretty Cures, he absorbs some earth to become bigger and stronger, but he also becomes immobile and defenseless. Kintolesky on the other hand subverts this trope. He's not dumb, but he hates strategy because he tends to fight straight and fair.
Gamao from Yes! Pretty Cure 5 is just a Lazy Bum who never keeps his part-time jobs, despite he needs money. And almost all of his encounters with the heroines are accidents.
Westar from Fresh Pretty Cure! is so unsuccessful with his plans that they sometimes backfire. One time, he manages to make people happy instead of desperate.
Akaoni from Smile Pretty Cure! just attacks without thinking. He believes that yokais from television are real and he doesn't recognizes the Pretty Cures at first when they unintentionally wear Paper Thin Disguises.
Gobukichi from Re Monster is the dumb muscle behind Goburou's party. He always takes the forward position to draw attention and tank while the other goblins finish off the prey at the right moment.
Ryu "The Owl" Nakanishi in Science Ninja Team Gatchaman. Though to be fair, he's not dumb so much as he's a simple country boy, and on a team consisting of two brains, a sophisticated bad boy and a charismatic ninja this tends to make him stick out like a sore thumb. (He has fallen asleep on the job more than once, though.)
Subverted by Gateau Mocha in Sorcerer Hunters; he's got the muscles and can be a bit of a silly party guy and a goof, but he's quite a bit smarter and more insightful than he lets on.
Jorgun and Balinbow of Tengen Toppa Gurren Lagann are twin examples of this trope, complete with excessive size, excessive strength, excessive enthusiasm, and a few hilariously demonstrated instances of both Hulk Speak and implied-to-outright idiocy. Contrast with Lordgenome, the series' resident Genius Bruiser.
Milly Thompson of Trigun is a female example of this trope. She's bigger than most men, carries a giant "stun gun", and tends to be dumber than the average housecat. However, this makes her Too Dumb to Fool fairly regularly. She also has a healthy dose of wisdom and emotional intelligence.
The Goats in Umineko no Naku Koro ni are certainly used more for their insane physical strength than for their wits. And this can backfire hilariously, as poor Virgilia finds out in Episode 4.