The Taming of the Grue

Monsters exist all over folklore. Dragons, vampires, werewolves, etc. And usually, they start out as Exclusively 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 the Metallic Dragons in D&D 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.

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.

To avoid ranting, examples list should only be those contained to be a single franchise or canon

 * Drizz't has fast-tracked the taming of D&D's Drow; although for the most part they're still evil antagonists, Chaotic Good renegade Drow 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 monster, albeit one you don't want to have to use. (So it's still a nuclear bomb metaphor.)
 * There are Cthulhu plushie dolls. Not to mention Hounds of Tindalos, gugs, Mi-Go...
 * In-universe example for Sam and Max. 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.
 * 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.
 * The oldest tales of Dragons (in the Western world) describe them as very large, very vicious reptiles, who may or may not have a penchant for eating maidens. The idea of sentient, sapient dragons that are not necessarily hostile to humanity is new, and might be consequence of cross-cultural pollination from Eastern conceptions of dragons.
 * There's always been the occasional dragon that could talk, in legends—at least back to the Migration Period in Europe—but they mainly used the ability to boast, make demands, or trick heroes. However, in some of the older versions of the St. George legend, he doesn't kill it, but baptizes it—meaning that dragon not only isn't a brute monster, it has free will and an immortal soul.
 * 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.
 * Djinn. In Arabic folklore they're basically the devil/devils. One Thousand and One Nights featured one being used by a protagonist to grant wishes. Now they're voiced by Robin Williams and helping people.