Note: since I realise this is a common trope for all sorts of kids stories, bonus points for people who can get one that isn't a kids story.

1. The Addams Family (opening pic)

I still find it so charming how the storytellers for this franchise took a family of vile murderous rogues and made a cozy feel-good story by drawing out their monstrous qualities and behaviours even further, rather than suppressing them.

1. Shrek

"Now ogres, oh, they're much worse! They'll make a suit from your freshly peeled skin. They'll shave your liver. Squeeze the jelly from your eyes! ...Actually, it's quite good on toast." - Shrek

The story that Shrek movies tell - of all the facets of acceptance - couldn't have been told without the monstrous identity of the lead character and several other characters in the franchise.

since I realise this is a common trope for all sorts of kids stories, bonus points for people who can get one that isn’t a kids story.

You want a wholesome, lovable monster who isn't in a kid's story? Easy.

One key to the film's appeal is that audiences like Hannibal Lecter...He may be a cannibal, but as a dinner party guest he would give value for money (if he didn't eat you). He does not bore, he likes to amuse, he has his standards, and he is the smartest person in the movie... He bears comparison, indeed, with such other movie monsters as Nosferatu, Frankenstein... King Kong and Norman Bates. They have two things in common: They behave according to their natures, and they are misunderstood. Nothing that these monsters do is "evil" in any conventional moral sense, because they lack any moral sense. They are hard-wired to do what they do. They have no choice. In the areas where they do have choice, they try to do the right thing.

Roger Ebert, quoted in https://en.wikipedia.org/wiki/Hannibal_Lecter

I hate hannibal lecter so much