I was reading the comments of this answer about what an orc would do if it found the One Ring, and realized the question of orc intelligence ought to be asked, and I found no such answer on this site.
Orcs are usually portrayed as stupid and evil. How accurate is this?
It seems to me that orcs are no more smarter, or dumber, than any other people. Gorbag seems to be a pretty smart orc, as seen in The Two Towers, Chapter 10, The Choices of Master Samwise:
'Who cut the cords she'd put round him, Shagrat? Same one as cut the web. Didn't you see that? And who stuck a pin into Her Ladyship? Same one, I reckon. And where is he? Where is he, Shagrat?'
Shagrat is no slouch, either:
Is that all you know of Her Ladyship [Shelob]? When she binds with cords, she's after meat. She doesn't eat dead meat, nor suck cold blood. This fellow isn't dead!'
It's harder to find examples of dumb orcs, actually. The goblins, which are smaller orcs according to The Hobbit, are the closest I can find. They aren't that smart given the descriptions, but not particularly stupid, either. They captured the group of dwarves, though they did it by surprise in the dark of night, and then they lost them to a wizard. Then they surprised the dwarves again, as told in The Hobbit, Over Hill and Under Hill:
they put out their torches and they slipped on soft shoes, and they chose out their very quickest runners with the sharpest ears and eyes. These ran forward, as swift as weasels in the dark, and with hardly any more noise than bats.
They weren't able to find or catch the invisible Bilbo, but they also didn't know or expect to have to look out for invisible people. They attempted to take the treasure left by Smaug and nearly succeeded, so that speaks to their logistical and strategic thinking to assemble such a large army so quickly.
Sure, in The Two Towers, The Uruk-Hai, the regular orcs want to spoil the prisoners and have fun, and don't want to do normal soldier stuff, but Ugluk and Grishnakh certainly seem to know what they are doing. The dumbest orcs were the scouts, that saw "Only a single horseman, and he made off westwards. All's clear now."
It seems to me that orcs are evil without question, but not necessarily stupid.
In the first instance, are we talking about the modern interpretation of Orcs, or Tolkien's original Orcs? As with many other fantasy creatures, the Orc concept has evolved (devolved?) over time, to the point where they're little more than a bunch of well defined tropes which few people dare to deviate from.
Assuming we're talking about Tolkien's Orcs: while I don't think the origin of these is ever confirmed, Frodo does comment that the Dark One can't create, but can instead only twist existing things. So the most likely explanation is that - as per Terry Pratchett's Unseen Academicals - they're a human subculture which has been subjected to magical warping and a heavily brutalised upbringing.
So, the answer to your question is another question: how intelligent are humans? There's certainly a wide variation across the entire world's population, especially in places where educational opportunities are limited.
In the second instance, my personal interpretation of Tolkien's Orcs is that they're essentially demonised industrialised workers.
More precisely, they're the sort of working-class people who were packed off to the WW1 battlefields to act as cannon fodder. You can see this in some of the later conversations which Frodo and Sam overhear:
‘Whose blame’s that?’ said the soldier. ‘Not mine. That comes from Higher Up. First they say it’s a great Elf in bright armour, then it’s a sort of small dwarf-man, then it must be a pack of rebel Uruk-hai; or maybe it’s all the lot together.’
‘Ar!’ said the tracker. ‘They’ve lost their heads, that’s what it is. And some of the bosses are going to lose their skins too, I guess, if what I hear is true: Tower raided and all, and hundreds of your lads done in, and prisoner got away. If that’s the way you fighters go on, small wonder there’s bad news from the battles.’
In fact, I don't think there's much evidence in the books to show that they're not intelligent; while Tolkien didn't exactly hide his dislike and distrust of anything which even vaguely looked like "modernisation", he did at least treat them as actual characters, rather than caricatures. Crude, brutal, and showcasing the worst aspects of industrialised city working culture maybe, but still actual characters with individual personalities, motivations and capabilities.
In the millennia before modern times there must have been hundreds, if not thousands of people born with the potential of a Newton or an Einstein; but they lived in a stone-age society or they were slaves, and never encountered a circumstance where their native talent could be developed.
Given that the orcs were either of corrupted Elvish or Mannish stock (depending on where Tolkien's thinking was at the time), any given orc could have fallen into the range of intelligence of any Man or Elf; but the environment in which they lived was brutal and not at all conducive to realizing their potential. The chief outlet for smarts was to be clever so that you didn't get yourself killed.
