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 should only be those contained to be a single franchise or canon.

Film

 * 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.)

Tabletop Games

 * Dungeons & Dragons regularly salvaged its Exclusively Evil creatures. At least, the good looking ones. But also have tendency of making snowclones of everything (again, see the dragons) ad nauseam, so the Good Counterpart / Evil Counterpart thing is at least as common.
 * 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.
 * On the upside, Al-Qadim fixed the genies. They tend to be larger-than-life, powerful and rather excitable, thus still can be scary even when they are nice. Other than this, Al-Qadim generally has people caring about whether a creature is Enlightened and/or honourable, while the Demihuman species matter mostly in terms of natural advantages and in context of marriage (in whether the given combination is known to be fertile), and consider doing otherwise a trait of barbarians.
 * Forgotten Realms has Ondonti - orc peoples who live as peaceful gatherers or farmers. Reports differ on whether they are a subspecies naturally not prone to rage that embraced a pacifistic religion (presumably after migrating to Faerûn via Orcgate with the rest) or common orcs long ago converted to teachings of the goddess of peace (who could tamper with their inherited qualities too). But in FR conversions go in every way - up to and including a gold dragon who ran into a great druid and was talked out of his overconfident righteousness (if not all the way to True Neutral).

Video Games

 * 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.
 * 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.

Multimedia

 * Lovecraft Lite is a big thing. There are Cthulhu plushie dolls. (There are chibi Cthulhu plushie dolls.) Not to mention Hounds of Tindalos, gugs, Mi-Go...
 * 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.
 * 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.