Played With in Changeling: The Lost as a sterotype of theOgreKith. Most Freehold leaders generally view new Ogres as this trope, and while there is occasionally some truth to this due to the Ogre's innate curse of getting less mentally adept as they grow magically powerful, it explicitly does not make them stupid. A genuinely dumb Ogre is actually extremely rare, and for good reason; few changelings escape from Arcadia and their True Fae captors with dumb muscle alone, and usually tricking the True Fae or bargaining their way out, and most sample Ogre characters in the books avert this trope.
To paraphrase Winter Masques, "A Gargantuan who spent forty years guarding the libraries of a Faerie Knight spent forty years reading those tomes."
Shadowrun plays with this; orks and trolls (races with higher physical stats) have lower intelligence caps than humans, elves and dwarves. Your average troll is no dumber than the average human, but trolls and orks can never be as smart as the highest possible peaks of human intellect. In the third edition intro to the races, the guest troll writer complains about the trope and claims that trolls and orks face discrimination and prejudice because everyone assumes this trope is true.
Earlier editions stated that orks and trolls weren't dumber than humans, just slower. As in, their thought processes were slower. Give a human and a similarly gifted troll an advanced mathematical problem and they'll both solve it, it'll just take the troll a bit longer.
In Warhammer there are lots of these. Orcs, trolls, kroxigors, sauruses and ogres can all be this.
In Warhammer 40,000, the semi-intelligent Fungal race, 'Da Orkz' fit this trope to a T. They're loud, they're strong, but they're not very bright. They do, however, tend to possess a certain animal cunning. In any case, Orkz which exhibit unusual intelligence are called 'Oddboyz', and would be outcast, if not for their obvious usefulness in a fight.
Ogryns, who are humans who have evolved into being very tall and strong, at the expense of their intelligence (which is about the same as an average ork). To make a revealing example, the ogryn Nork Deddog is a genius by his race's standards, as he can write his first initial of his name, speak in full sentences, and count on up to four using his fingers (his thumb confuses him). The Imperium is quite fond of them due to their Dumb Is Good philosophy, in addition to their great size and strength for a non-Space Marine human, making them powerful, loyal soldiers.
The small mind is easily filled with faith. One of the main reasons ogryns are allowed to join the Imperium and not destroyed as mutants is their unquestionable faith in Emperor. They are simply too dumb to think about betrayal. In cases of Chaos-corrupted ogryns it's always their leaders who turn to Chaos and then lie to ogryns. They still think they are fighting on the right side.
In FATAL, if your intelligence is under a certain level, you can end up with a sizable strength bonus. This being FATAL, they actually call it "Retard Strength".
Of the player races, Half-Orcs are consistently portrayed in this fashion; they get a bonus to their Strength scores, and in 3rd Edition, a penalty to Intelligence.
Of the classes, Barbarians fit the mold better than any other. Before 4th Edition, anyone rolling a Barbarian had to spend points for their character to know how to read. Naturally, the popular Half-Orc Barbarian is often both a mental midget and a paragon of power. Meanwhile, the Fighter of 3.5 is actually something of an aversion: though they're free to dump mental stats, one of the best feats in a Fighter build, Improved Trip, requires an above-average Intelligence of at least 13.
The Orc god of strength Bahgtru is stupid even by Orc standards with one of his nicknames being "the awesomely stupid." He is so stupid, intelligence draining attacks have no effect since he cannot get any dumber. On the other hand he is so strong he is immune to strength draining spells and can bypass spells that protect from physical damage. Weapons and armor only slow him down, and he is never depicted using either in any myths, instead pummeling legions of enemies into paste with his bare hands; the symbol associated with him, a broken femur, comes from a famous orcish myth where he slew a giant, hundred-legged monster from another dimension by breaking all its legs.
A lot of monsters fit the profile of dim-witted thugs, if you go by stereotypes, including ogres, hill giants, trolls, and minotaurs (except minotaurs on Krynn, who can be rather smart).
In Orcworld, the orcs' war god is the ultimate in this, so stupid he actually tells a dragon that he doesn't care whether he woke him up. At one point his (much weaker) Pugg openly says, "It's true, he knows nothing." and he doesn't even realise the insult.
In Blood Bowl, most teams can hire at least one "Big Guy." With only a handful of exceptions, they all have either the Bone-head, Really Stupid, or Wild Animal traits, which means they are liable to stand around and do nothing for a turn. Even more of them have the loner trait, which means they can waste rerolls.
Paranoia: Internal Security likes to promote these types straight to Green clearance. The goons love the authority, plus they act as a Hate Sink to distract attention from their superiors. "You're thinking, 'They sound like orcs'. Nope— these are orcs you're not allowed to kill."