The Taming Of The Grue
Always Chaotic Evil as they come, or even just mindless beasts who destroy because they don't know any better. Except, as a particular monster gets more popular, it has a tendency to get less... monstrous. Dragons - which at least in Western mythology were once giant, winged, fire-breathing lizards that burned villages and were slain by knights - first got more intelligent, then more likely to be a "not really a monster" subversion, until, in the modern era, stuff like Dragonheart and Pete's Dragon are nothing to bat an eye at. Similarly, orcs - who were invented for The Lord of the Rings to be bred evil (and mostly stupid) often appear as "noble savages" after just eighty years. There are also cases where said monster is modified in order to appeal to younger demographics by making him more cute, huggable, and so forth. In short, this trope is Villain Decay on the species level - what happens when Our Monsters Are Different turns the exception into the rule. See also You Sexy Beast, Lovecraft Lite. Friendly Neighbourhood Vampire is a subtrope of this.
To avoid ranting, examples list should only be those contained to be a single franchise or canon:
- Drizzt Do'Urden has fast-tracked the taming of Dungeons & Dragons' Drow; although for the most part they're still evil antagonists, Chaotic Good renegade dark elves are a trope of their own by now.
- Godzilla began as a horrible monster and nuclear bomb metaphor. Later on he became a protector from the other monsters, and for a while during the '60s and '70s, completely heroic, before being re-tooled as still a defender, albeit one you don't want to have to use. So it's still a nuclear bomb metaphor.
- There are Cthulhu plushie dolls (as shown in the page image). Not to mention Hounds of Tindalos, gugs, Mi-Go. Moreover, recent fiction is much more likely to play these guys for laughs rather than straight.
- In-universe example for Sam & Max: The Devil's Playhouse. Turns out that back near the beginning of our planet's existence, molemen were powerful, destructive creatures who could successfully fend off Eldritch Abominations. They didn't evolve well.
- Werewolves have this problem, on and off. Old folklore describes them as vicious animals, at best, but contemporary works tend to humanize them more. They still get cast as vicious animals, but their humanity is still more pronounced. Some traditions have werewolves as a type of witch who sold their soul for their ability to transform, so even as human beings they were evil. Modern werewolves tend to either be innocents who contracted the curse by being the victim of another werewolf, or having been born that way (and usually possessing some degree of control). Either way, they can't help what they are.
- The softening of the Werewolf dates back as the 12th Century where Marie de France writes the tale of the Bisclavret who was trapped in his Wolf form by a treacherous wife after revealing his secret and is captured then kept as a pet by the King who he remains loyal to, even as a Wolf.
- Vampires can be more or less human, and more or less hostile to non-undead, depending on the writer. In recent times, with growing popularity of Vampires Are Sex Gods, they've gotten a bit softer. See Friendly Neighbourhood Vampire.
- The trope namer, grues, first appeared in Infocom's classic Zork games as the unseen (and, because they never leave pitch-dark areas, unseeable) monsters who would eat adventurers careless enough to wander in dark places without a light source. Later works such as Wishbringer and Zork: The Undiscovered Underground would play grues for laughs; Wishbringer featured a grue lair with a refrigerator whose light goes out when you open it and a mother grue with an apron, while Undiscovered Underground had a grue convention where grues would discuss topics such as 'Surviving the lean years'. The grues were still dangerous, but played less seriously than in earlier works. The once-popular humorous wiki Uncyclopedia pokes fun at grues even more, making them look like the weird Japanese character Domo-kun for the hell of it.
- Zombies and Skeletons while never portrayed as cute or cuddly, in cartoons it's not uncommon see friendly zombies and skeletons, who can detach and attach their parts at will. Then there are movies such as Hotel Transylvania, Daddy Im A Zombie and Corpse Bride (In which the undead were much more lively and upbeat than the extremely dreary land of the living) and of course the Monster High franchise. Even then there are fantasy novels and videogames which may feature Zombies who are friendly but either wish to be accepted by humans, or wish to die due to seeing themselves as monsters. Subverted in Fallout in which the "Zombies" aren't actually zombies (And don't use that word in front of them) but are humans mutated by radiation to look like a corpse, but if their brain become radiated enough they can become "feral" and act like typical zombies.