It's big, powerful and nasty. It's not humanoid, but familiar all the same.
This trope is for Eldritch Abominations that either naturally resemble (somewhat) ordinary animals, or else possess Animorphism and spend a good deal of time in the animal form.
The Beast, Gut's Enemy Within and possibly the sentient incarnation of his hatred and rage (and boy does hehave a lot of both) usually takes the form of a large canine with lightning bolt-shaped eyes. The Berserker armor's helmet, which was previously skull-shaped, now resembles its face when Guts wears it.
Several Apostles also have animalistic One-Winged Angel forms as well, most notably Zodd (pantherlike minotaur), Rosine (gigantic moth), and the Count (humongous slug).
In Animal Land, the Chimeras that Giller uses are unnatural monstrosities that aren't anything compared to the relatively natural-looking animals of Animal Land. A number of them look more like they come from Berserk than a lighthearted animal manga.
The Beast Titan from Attack on Titan does not resemble a human as much as other Titans do, being more reminiscient of a gigantic sasquatch. It's also shaping up to be the Big Bad, and the only REAL Titan we've seen, as well as the fact that it can turn humans into Titans. Oh, and It Can Think, talk, and command lesser Titans.
Many paintings by Salvador Dali are famous for depicting horses, elephants and similar animals with spindly, enormous legs and other nightmarish features.
Films — Animation
Fantasia: the title entity from "The Firebird Suite".
Films — Live-Action
In The Thing, the monster spends most of its time as an Alaskan pack dog. You catch a glimpse of what it really is, before it proceeds to eat all the other dogs. It also appears very much like a spider/insect-like organism in the prequel and in Carpenter's movie it still retains arthropod features like random insect legs. More horrifyingly, in the novel that inspired all of this, it is also heavily implied it assimilated an albatross, so it can now fly. That said, there's no way of knowing what it really looks like, if it even has a "true" form at all, rather than being purely amorphous.
King Ghidorah, archenemy of Godzilla is what happens when the villain of a Cosmic Horror Story comes in the form of a giant golden dragon with three heads and a penchant for exterminating entire planets.
The eponymous monster from Lair of the White Worm is a giant snake-like dragon (the word "worm" meant dragon originally) and is worshipped by a race of reptilian vampires.
Many monsters in Lone Wolf would fit this. Most notable is Demonlord Tagazin, who appears as a huge sabertoothed jackal.
Mogget and the Disreputable Dog from the Old Kingdom trilogy. Respectively, Yrael and Kibeth the Bright Shiners.
Clark Ashton Smith's "The Seven Geases". The Cthulhu Mythos deity Atlach-Nacha resembles a huge, hairy and hideous black spider. From the same author, we also have Tsathogghua and its extended family, who tend to have batrachian looks.
From Sword of Truth, the Chimes of Death, for whatever reason, take the forms of chickens.
In Neverwhere the Beast of London is believed to have started life as a runaway pig from a butcher; centuries of feeding on sewage and its own vileness has made it much, much more than that.
Thunderclasts (giant dog-shaped monsters of living stone) and Midnight Essence (animated smoke contained within a skin vaguely like that of a weasel) in The Stormlight Archive: Also possibly the chasmfiends, enormous creatures like carnivorous lobsters the size of a largish apartment building. They are natural creatures (aside from having to use a bit of magic to get around the Square/Cube Law), but still nasty and scary.
Dragons from A Song of Ice and Fire. No, really: particularly if you go with the "fire made flesh" idea that has been posited in-world. These dragons can feed on human breast milk. They need to eat cooked meat rather than raw (it's not just a preference). They have a protracted "childhood" in that, well, they never really stop growing or developing unless imprisoned. And, if you step back and don't charge in like Leeroy Jenkins on a bender, can actually be understood, be trained and bond with (preferred) humans far better than you'd expect for creatures that look so magical and reptilian. In short: their psychology isn't an exact match... But, it's far closer to "social ape" than you'd assume at first glance. Lost Targaryen lore might just have boiled down to a good book on how not to screw up around dragons (also, how to fit them on a naughty step, time your bribery and incubate their eggs properly), rather than anything particularly esoteric. Minus the mystic bonfire with blood-sacrifice and death aspects involved in egg-hatching or the whole "blood of about the temperature of molten copper" thing, of course.
The titular "Sun Dog" from Stephen King's Four Past Midnight is closer to this than a dog. A Magic Camera will produce pictures only of the dog, and each one is slightly different. It becomes clear that they form a sequence; the characters can flip through them like a flipbook and watch the dog move, and they can even be transferred onto film to create a short movie. Either the dog or the camera is able to exercise More Than Mind Control to trick users into taking more and more pictures, and the more pictures that are taken, the closer the dog comes to escaping... and the less like a common dog and more like this trope it becomes.
From Judeo-Christian myth come the Ziz and the Leviathan. Also the Second Beast from the Book of Revelation, which is described as bearing many crowns atop many heads, and is variously depicted as as being draconic, catlike or serpentine. Beelzebub and Amon are also noteworthy examples.
Shadowrun has a lot of these in the form of magical beings like the totem Spider which plots world domination and manifests as a huge spider in astral space, and the Sega Genesis game has Thorn, a dog or coyote-like malevolent spirit.
RuneQuest. In the Glorantha campaign setting one major empire has an enslaved Chaos god/demon/thingy called the Crimson Bat, which looks something like a giant bat.
Two of the Elder Evils from Forgotten Realms—Dendar the Night Serpent and Kezef the Chaos Hound (based on the Midgard Serpent and Fenris Wolf from Norse Mythology).
Pathfinder's Rovagug bears more than a slight resemblance to a centipede, albeit one large enough to undo creation.
Many behemoths in Exalted resemble gigantic monstrous versions of animals, which are implied to have come first; there are references to "animals and the behemoths they were based off of".
Most of the Yozis resemble gigantic environments with many also having forms that resemble strange and transcendent humans, but Isidoros usually has the form of a monstrous black boar with innumerable tusks, great many-lobed eyes and thick barbed hairs, so large that his hoof prints are canyons and his back brushed against the sun, moon and stars.
This is also a possible fate for chimeric Lunar Exalted.
Phyrexia has strange ideas about what constitutes a creature, Green-aligned New Phyrexia in particular. As a matter of habit, Phyrexia swaps and recyces body parts between organisms, living or dead, organic or otherwise, with little regard for whether or not what they're making actually needs those parts. For example, the Rot Wolf; if you look closely◊, you can see that it does not contain any actual wolf.
Witherfang, the giant wolf commanding a tribe of werewolves, is presented to you as one of these at first. It turns out, however, that it is merely a wolf body possessed by the spirit of the forest it lives in—and one of the most human characters in the entire game.
The Old Gods of the Tevinter Imperium count as these, especially after being transformed into Archdemons by the Taint. The Old Gods supposedly taught the Tevinter Magisters the secrets of Blood Magic, and making offerings at the altars of the supposedly long-dead ones still rewards worshippers with gifts of power. While the Archdemons look like a mix of Darkspawn and Dragon, they are something else entirely. This is why weapons that do extra damage to Darkspawn/Dragons are not especially effective against the Archdemon in the first game.
The Beast in chapter one of The Witcher is a huge dog-shaped manifestation of the collective sins of an entire village, materialized to haunt and terrorize them.
A lot of the monsters from Silent Hill resemble animals. Dogs, cats, bird-bat things, roaches, and a crocodile have all been demonstrated.
From the same game, the Gohma also qualify. They resemble demonic versions of various animals with black skin and massive red veins all over their bodies and the smallest and weakest one of them is a gorilla.
The Liir of Sword of the Stars resemble dolphins or whales with a number of features from other sea creatures (fur, tentacles, negligible senescence...) and Psychic Powers, but most of them are simply Starfish Aliens. The Suul'ka, on the other hand are bigger than most starships, feed on the life-forces of planets, are summoned from the black depths of space where they slumber by mass sacrifices, and have a method of "teaching" their followers via direct telepathic contact that is almost always fatal for the follower. They're actually incredibly ancient Liir gone mad with power who've decided to take the Galactic Conqueror route.
Many of the later legendary Pokémon, especially Dialga, Palkia, Giratina (who personify time, space and anti-matter) and Reshiram, Zekrom and Kyurem (who were once a single dragon who may or may not have come from space).
Mewtwo could also count, even though he's a bit more human-shaped than the dragons.
Groudon, Kyogre, and Rayquaza really started the whole trend. Mewtwo was astoundingly powerful and dangerous, but was of entirely artificial origin, while Ho-oh and Lugia were, again, monstrously powerful, but while the former possesses abilities that certainly approached demigod territory, the latter was mostly just an exceedingly strong monster who stayed away from humanity. Groudon and Kyogre, on the other hand, are astoundingly old, slumber in places well beyond the reach of man, and can literally shape the world with their powers, and awakening them constitutes an apocalyptic event that could quite possibly wipe out all life on the planet. Rayquaza, meanwhile, is their mediator, which is to say that when those two have their squabbles, it swoops in to break it up and keep the planet from being flooded or reduced to a barren rock, and while it doesn't have the Walking Wasteland attributes of the other two, it's still frighteningly powerful and beyond the reach of man.
In Kingdom Hearts lore, all beings whose hearts become tainted with the power of Darkness become Heartless monsters. Most Heartless are mindless beasts with no resemblance to their original self. Very rarely, a Heartless will retain its original form and mind. The two canon examples of this are the human Big BadXehanort... and, for some unknown reason, the lion Scar.
The Alpaca in Alpaca Evolution becomes increasingly Lovecraftian as it assimilates other alpacas, angels, and even God.
Becquerel and the G-Cat from Homestuck are First Guardians, giving them Reality Warper powers. Justified: They have the First Guardian genetic code, but were otherwise cloned from ordinary Earth animals. Trolls with the power to psychically command wild animals can use it on Bec and G-Cat.
We Are All Pokémon Trainers has ♨č▒⢫╠␣☣ł₤舸▟, or the Glitch Nidorino, a representation of the fear of death that merely takes the appearance of the first being it encounters in the material world, in this case being Vinollo the Nidorino. Luckily unlike most other Glitches it's friendly if its mission isn't to beat the fear of death into you.
Avatar: The Last Airbender has a couple of the spirits, including Koh, a giant centipede with a face that can change from human to animal to just about anything. And WanShiTong, a giant owl with an extendable neck.
The Legend of Korra continues this trend with the spirits of light and dark, Raava and Vaatu, which resemble gigantic flatworms.