Where the Wild Things Are: The titular Wild Things are so exaggerated and silly, you just want to hug them all. Generally speaking, Maurice Sendak practically runs off this.
Interestingly, adults seem to be put off by the Wild Things' appearance more than children. This was a major talking point when the film was released; just what side of the "It is for kids" / "It's not for kids" divide does it fall?
Many Redwall fans think the villainous "vermin", who are supposed to be ugly and creepy, are cuter than the good "woodlanders".
It's hard not to agree with them at times: compare a hare◊ (good) and a ferret◊ (vermin). There have been some alternative arguments as to how Jacques draws the distinction between good animals and bad animals, the most popular being that it's based on the literal definition of vermin. But that doesn't explain anything since nearly all the good animals are also vermin. So no one really knows except Jacques himself.
It generally seems to be based on contemporary urban British perspectives of the animals, which explains the relative ambiguity of wildcats and foxes (although the popularity of ferrets and rats as pets in recent years dates the series slightly). To people in a rural environment, of course, they would all be vermin, except the hare, who would be lunch.
People say he makes the cute animals good. This is a blatant lie. EVERYTHING in Mossflower is cute.
The best way to describe this is, "some readers will see their appearance based on their personality (If they act evil, they'll look more evil to those readers) while other readers still see them as their real-world counterparts regardless (Fluffy and adorable)"
Dobby and, in general, the House Elves from Harry Potter. Even Kreacher gets better.
Alan Rickman's portrayal of the character likely contributed to Snape's woobification. In the books, the character only becomes sympathetic after he dies.
The Thestrals - well, for those who can see them, anyway.
Then there's Crookshanks, the ginger cat, who is described as having a sort of squashed face. And yet Hermione adores him.
The Hunger Games has a similar case with Buttercup.
The Other, the sentient operating system of Otherland, steals system resources to create a private world for itself, populating it with grotesque mockeries of fairy tale creatures that are nevertheless treated like its children. This is not out of malice, but because it genuinely doesn't understand the context.
This isn't uncommon in Lovecraft Lite in general. It helps that much of the horror fandom doesn't share Lovecraft's apparent aversion to sea life.
Lovecraft's own Zoogs, by virtue of being small, furry, and tentacle-faced.
Some illustrators draw Brown Jenkin (the little human-faced monkey-rat-imp familiar from Dreams In The Witch House) this way before events in the story start getting really sinister. Lovecraft depicts him as a denizen of the Uncanny Valley, but anything small, furry, and vaguely anthropomorphic is going to be cute to someone.
Aunt Beast in A Wrinkle in Time. She's part of the "really, really strange looking - but still sweet and lovable" side of this trope. In Wayne D. Barlowe's portrait of Aunt Beast, she's downright lovely - in a very alien way.
Practically any artist's representation of an Ixchel is likely to fit this trope.
All the characters in Tim Burton's The Melancholy Death of Oyster Boy: And Other Stories.
The more A Song of Ice and Fire harps on just how ugly Brienne of Tarth is, the more you just want to...hug her. That she's one of the most good-hearted characters in the series just makes her that much more adorable.
The books also have Tyrion Lannister, who is also one of the more likable characters in the series (although more morally ambiguous than Brienne), and even less conventionally attractive.
According to Oberyn Martell, his dead little sister Elia coo'd at him when he was a baby.
Also Shireen Baratheon: a child which combine the worst traits a girl can inherits from her parents with a childhood disease which disfigured her. She's a quiet, sad little girl that never smiles.
There's also Pia, a serving maid from Harrenhal, who was pretty until she made the mistake of being within arm's reach of Gregor Clegane, who broke her nose and most of her teeth.
Death himself, for that matter. He's your stereotypical cowled-skeleton-with-a-blade Grim Reaper, and plenty badass when he needs to be, but he's a gently compassionate being who loves cats, makes endearingly misguided efforts to understand humanity, and rides a Pale Horse named Binky.
Vettul, in the Doctor WhoEighth Doctor Adventures novel Vanishing Point, is a twenty-year-old ingenue who's at least 6'6" and has one leg twice as thick as the other, obviously crooked eyes, and an otherwise plain face. She also acts like she has No Social Skills, in a completely endearing manner, and manages to have Incorruptible Pure Pureness without being cloying. She quite fancies Fitz (and calls him "very beautiful", at which he "[stands] there speechless, blushing crimson", being only average-ish in the looks department), and he her:
She looked like a painting of someone beautiful that had gone subtly wrong somehow; as if the artist had been wearing the wrong prescription glasses or something. That said, there was definitely something to her...
She lives with a group of other people who have various (worse) deformities, and would therefore be persecuted in the dystopia where they live, and their caretaker, Ettianne:
A little man with a bent, frightened face peeped out from behind a table, and Ettianne went over to soothe him.
Pretty much the entire crew of the Ferkel in Rod Allbright Alien Adventures. None of them (save perhaps Plink, and Edgar if you want to count him) are conventionally cute. All are teribly, terribly endearing, particularly Snout.
Played with in the Lensman series. Ordinary stay-at-home humans find the various Starfish Aliens to be utterly horrible-looking (and likewise for ordinary stay-at-home aliens wrt humans), but cosmopolitans, spacehounds, and especially Lensmen are expected to rise above this. In particular, Kinnison and Worsel have a very strong friendship, saying about each other: "He's so hideous that he's positively distinguished-looking."
Candayce, in the body of a Leptoceratops, starts to think this of the Leptoceratopses which seem enamored of her, and of their babies, after initial difficulties in Dinoverse.