1. Ape, Carnivorous: "Low (upper)" (7). The ordinary ape, listed as "Ape, (Gorilla)", has Low (5-7) intelligence, but its "larger, stronger and very aggressive relative" is at the upper end of that range, having a "fair intelligence (IQ 70+) and being "very cunning". Disturbingly, these smarts correspond with a sinister craving, as it "hungers particularly for human flesh"...
2. Beaver, Giant: Low to Average (5-10). While the other unusually-sized rodent in this book, the Giant Rat, is only semi-intelligent, the Giant Beaver at the high end approaches the average for human intelligence, i.e., 10.5 on a 3-18 bell curve. Furthermore, their description indicates an interest in coins, trading, and building dams for profit, which means that they are essentially an unexpected and woefully underused NPC race for characters to interact with. The details in the Monster Manual go back to the original writeup in the Blackmoor supplement, which also includes "gourmet bark" (!) in the list of valuables they will trade for. Dan Boggs has speculated in a post on ODD74 that they were one of the monsters written up by Dave Arneson himself. To me, they feel like an amalgamation of the prehistoric giant beavers that existed in the U.S. until relatively recent times, which were similarly 6 feet long, and Mr & Mrs Beaver from The Lion, the Witch and the Wardrobe.
3. Beetle, Boring: Animal (1). With six different varieties of giant beetle, each one needed a distinguishing trait, and for the Boring Beetle this feature is a hive mind. Thus, alone among beetles, the Boring Beetle has an intelligence score above zero, which fuels alternative-agriculture skills in the form of farming "molds, slimes and fungi substances", and (per rumor, but in D&D the monster rumors are always true, right?) developing "a communal intelligence which generates a level of consciousness and reasoning ability approximating that of the human brain". As with the Giant Beaver, these details go back to the Blackmoor supplement, and likely Arneson, which elaborates on these farming practices: they grow "yellow mold for food, as well as cultivating many of the other vile jellies and slimes often encountered in dungeons" and "[t]hey start their nauseating cultures by gathering various dead bodies and rotting offal and add a small bit of the substance to stimulate growth (sort of putrid Petrie dishes)" I think the implication here is that their practices are partly responsible for the "the clean-up crew" being so prevalent in dungeons! Not quite so, ahem, boring?
4. Dolphin: Very (11-12). While everyone knows that Dolphins are on the intelligent side for animals, in D&D they boast a score above the average for humans, and towering over their underachieving cetacean kin, the whales, who can only boast a score of Low (5-7). Furthermore, ten percent of dolphins go so far as to form "underwater communities" that are sufficiently organized to employ guards from other species, such as swordfish or narwhals. This is yet another creature first written up for the Blackmoor supplement, but Boggs places their authorship with contributor Steve Marsh, later thanked in the Monster Manual for "for devising the creatures for undersea encounters which originally appeared in BLACKMOOR". The original writeup places even more emphasis on their "great intelligence", as they can communicate with other dolphins using telepathy, and in battle employ a "war harness", a rig with "a long wicked spear that protrudes in front"...!
5. Gray Ooze: Animal (1). Most of the clean-up crew cohort are non-intelligent, including Black Puddings, Gelatinous Cubes, Green Slimes and Ochre Jellies, but the Gray Ooze is a slightly higher order of creature, having animal intelligence. And with great size they can transcend even this modest brain-power: "In exceptionally large individuals an intelligence of a sort is well developed. Furthermore, these exceptional individuals have a latent psionic ability..." that includes a psychic crush attack. This ability was first added in an entry in Eldritch Wizardry in the section on Psionics. Now you are now probably wondering, "Do psionic Grey Oozes dream of deliquescing sheep"?
6. Invisible Stalker: High (13-14). In OD&D, these were "an extra-dimensional monster" conjured by the 6th-level magic-user spell of the same name, but here they are revealed to be from the Elemental Plane of Air. Unlike their clerically-summoned cousins, the Aerial Servants, who are only semi-intelligent, or garden-variety Air Elementals, who are of low intelligence, the Invisible Stalker is extremely bright, which is probably why they so often resent being whisked from their home to do a magic-user's grunt work. Note that the entry for Air Elemental also indicates that on the plane of air are "certain intelligent air elementals which have special abilities beyond the above".
7. Lynx, Giant: Very (11-12). See Tom Wham's cartoon at the top of the page, which sums it all up much better than this wordy blog post.
8. Mimic, Lesser: "Semi- to Average" (2-10). Mimics have a much wider range in intelligence than most monsters because, as the text reveals, there are actually two types: the larger "killer mimic", which is only semi-intelligent and "the slightly smaller, intelligent sort". The smart ones are "generally friendly if offered food", which is a rare instance of the Monster Manual using the term "friendly" in reference to a non-humanoid monster, and even better, they may "tell a party about what they have seen nearby". To aid in this advanced food-gathering tactic they have evolved a facility for languages, typically being able to speak "several other tongues such as common, orcish, etc" in addition to their own.
9. Mold, Yellow: "Non- (see below)" (0). While the typical Yellow Mold is not a deep thinker, or even a thinker at all, here size once again begets unexpected brainpower: "When formed into great colonies of at least 300 square feet in area this growth will form a collective intelligence about 1 time in 6. If this should happen the yellow mold will be aware mentally and psionically" and can attack equivalent to "the most powerful form of id insinuation." As with the Grey Ooze, this ability was first noted in Eldritch Wizardry. In addition to a psionic attack, the mental awareness suggests the colony might be communicated with via telepathy, assuming you took "Yellow Mold" as one of your languages.
10. Neo-Otyugh & Otyugh: Very (11-12) & Average (8-10). I've combined these because they obviously should have been one entry in the Monster Manual like the Mimic. I mean, the Neo-Otyugh entry is basically just: "bigger and smarter otyugh". These creatures dwell in the same ecological niche as the trash compactor monster in Star Wars, although they were published first, with the Neo-Otyugh appearing in the 1976 tournament version of the Lost Caverns of Tsojconth (see a pic here at the OSR Grimoire). Nobody expects a trash monster to be an Einstein, but unexpectedly the Otyughs are often as smart as the average human, speaking their own language and being "semi-telepathic, thus often able to communicate with other life forms when the otyugh so desire". Which is presumably useful for telling the boss when the dungeon septic tank needs to be cleaned out.
11. Octopus, Giant: Animal (1). While only a single point smarter than their dimmer cousins the Giant Squid, Gygax casts these overgrown cephalopods in a completely sinister light that appears to hint at even greater mental prowess. Specifically, they have an alignment of "Neutral (evil)", are "malicious", have "a cunning intent" and can form gangs with other members of their species "to overwhelm a larger ship if the opportunity presents itself". This evil disposition is a distinct change from their earlier writeup in the Blackmoor supplement, where they were "generally peaceful" and only attacking ships "after provocation".
12. Owl, Giant: Very (11-12). While less unexpected than the other entries here in view of the association of owls with intelligence, giant owls "will sometimes befriend other creatures" and "speak their own language". A value is still given for their eggs, because humans are horrible.
13. Roper: Exceptional (15-16). This living stalagmite with octopus arms turns out to have the highest intelligence of all the monsters in this list, being way smarter than most humans. It was originally written up in Strategic Review #2 in very similar format, including a "Highly Intelligent" stat. There is no further mention of this intellect in either source, but it goes to show that in D&D, one would be foolish to underestimate "a mass of foul, festering corruption".
14. Shambling Mound: Low (5-7). Being a walking pile of swamp moss, one might expect a score of "Non-" here, but no, "Shamblers" (in Gygaxian slang) are actually smarter than a number of Fighters, as per the AD&D Players Handbook, with an intelligence of 5 or lower one can only be a Fighter. There's no other mention of any particularly brainy behavior, but I'm guessing that this score is a result of its comic book inspiration ala Swamp Thing, Man-Thing or the Heap.
15. Slithering Tracker: Average (8-10). This awesomely-named, plasma-draining, cleaning-crew-adjacent monster is often overlooked, most likely because there is no picture of it (but see the never published one here by Bill Willingham). They are much smarter than any of their relatives, perhaps having evolved such intelligence to aid in tracking their prey. A candidate for your next ranger character?
16. Spider, Giant, Phase & Giant Water: Low (5-7) or Semi- (2-4). Spiders in general follow the trend noted above of "bigger is brighter": Large Spiders (HD 1+1) are "Non-" (0), Huge Spiders (HD 2+2) are "Animal (1)", Giant Water Spiders (HD 3+3) are "Semi- (2-4)" and Giant Spiders (HD 4+4) and Phase Spiders (HD 5+5) are "Low (5-7)". There's not much elaboration on the intelligence of the Giant or Phase spiders in their entries, other than that they will flee superior foes (Giant Spiders) or that they will (in more erudite fashion) "seek to evade encounters which are unfavorable" (Phase Spiders), which based on their powers brings to mind Bilbo using the One Ring to avoid unwelcome visitors at Bag End. Giant Water Spiders, despite being only semi-intelligent, exhibit the most interesting of the noted spider behaviors, being approachable if offered food, and thus occasionally becoming pals with aquatic folk like nixies.
17. Strangleweed: Animal (1). Nobody expects an "intelligent kelp". Need I say more...? This is another undersea encounter originally devised by Steve Marsh for the Blackmoor supplement, although the word intelligent does not appear there.
18. Toad, Ice: Average (8-10). This oft-overlooked variety of overgrown amphibian has almost human-level intelligence, which is much, much higher than the "Animal (1)" intelligence of the typical Giant Toad. Furthermore, Ice Toads even have their "own weird language", which might prove useful when asking them for directions to the Glacial Rift of the Frost Giant Jarl.
19. Trapper: Highly (13-14). As this creature is the dungeon-floor counterpart of the more awesomely-named Lurker Above, one might predict a similar "Non-" intelligence, but instead the Trapper is a good degree smarter than the average human. This is perhaps an evolutionary necessity to stay ahead of all those suspicious adventurers. They are further described as "clever" and able to create a "protuberance which resembles a chest or a box", perhaps suggesting a relation to the more intelligent breed of Mimic (see above).
20. Wolf, Winter: Average (8-10). As with the Giant Lynx and Ice Toad, the Winter Wolf is a cold-climate species that is more intelligent than its temperate-dwelling relatives; in this case, both regular and dire wolves, each of which are only semi-intelligent. Winter Wolves are even a cut above the low-intellect Worgs, which based on Tolkien alone one might predict would possess a bit of cunning. What is it about the arctic that fosters intelligence in Gygaxia? As with the other arctic-intellects, they speak "their own language", but being "Neutral (evil)" and having a "foul disposition", I'm sensing a cultural rivalry with the neutrally-inclined Giant Lynx and Ice Toads.
Honorable mentions (since I wanted to keep the above list to 20 entries): Perytons and Umber Hulks, each of "Average (8-10)" intelligence, and each speaking their own language. Perytons were new for the Monster Manual, but Umber Hulks were first written up for the Greyhawk Supplement, but without any note of intelligence or language.
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