D&D Monsters: Frost and Fire Giants

Both frost and fire giants, as portrayed in D&D, are loosely based on the jötunn of Norse myth. In the original myths, this was a rather vague term referring to a race of mostly (but not always) gigantic beings originally created by the primordial being Ymir. Ymir himself was certainly gigantic, since the sky is said to be the inside of his blue-coloured skull, and he was also described in the Prose Edda as "ice cold". Thus, while frost giants aren't a specific thing in Norse myth, it's clear where the idea comes from. Fire giants, apparently also descended from Ymir in the original myth, are the inhabitants of the fiery realm of Muspelheim, led by Surtur, whose primary function in the myths is to destroy the world at the conclusion of Ragnarok.

Both frost and fire giants appear in a range of fictional sources, of which perhaps the most obvious are the Mighty Thor comics. These predate D&D by over ten years, although it's likely that their appearance in the game is an independent creation from the same mythic origin, since they're quite clearly different from the comicbook versions. In D&D, they are the third and fourth rungs on the six-step ladder of increasing giant power and strength and are portrayed as more technologically advanced than the smaller hill and stone giants.

D&D Monsters: Hill and Stone Giants

Giants are a recurring figure in myth and folklore, appearing in the stories of just about every real-world culture. There's something fundamental about the idea of people who look vaguely like us but are much larger and stronger. There is, of course, considerable variation among cultures as to what giants are supposed to be like, and even D&D reflects this by having six different core types, even before we get into one-mention specials or other creatures that are, in some sense, gigantic humanoids (such as ogres).

As is common where variants of the same idea for a monster exist in 1E, the six basic giants are arranged in a clear hierarchy of power, with each type having one extra hit dice, one extra point of strength, and delivering one extra die of damage than the one below it. Unlike some other creatures, while the details change, this progression of power remains the same in later editions. 

D&D Monsters: Bulettes

The bulette is a creature original to D&D. Like the owlbear, it's based on a plastic toy from Hong Kong, in its case probably meant to represent some sort of kaiju, although it's hard to know for sure. It's one of a minority of original monsters to have an actual name right from the start, rather than a descriptive term ('mind flayer', 'carrion crawler', 'trapper'). 

Incidentally, Gygax originally intended the word to be pronounced as "boo-lay", and official material from WoTC, and TSR before them, used to insist on this - and maybe still does. This raises a question, often seen in fantasy literature more generally, of "then why didn't you spell it that way?" In this case, I'll note that both the spelling and the supposed pronunciation appear vaguely French, which may be intentional - although, obviously, they don't match up with one another in that language either...

D&D Monsters: Stirges

The strige is a creature of Roman myth, derived from the earlier Greek strix. It was said to be a nocturnal bird, albeit one that hung upside down like a bat, which drank the blood of infants and possibly even ate the remains. The Greek version of the name has since been adopted as a scientific name for a genus of owl, and, blood-drinking aside, the general description does seem to match owls more than anything else that might exist in the real world. The name later also became associated with witches and with a more humanoid form of vampire, the strigoi. 

In D&D, of course, the name mutates again to the form "stirge". While it looks even less owl-like than the mythic creature, it's still clearly based on it... but is more inclined to attack adults than babies.

D&D Monsters: Manticores

Manticores are creature not of Greek, but of Persian, myth. The name literally means "man-eater", and it's at least possible that it originated with a "traveller's tale" style exaggeration of man-eating tigers. They were supposed to be hungry for human flesh - something retained in D&D - and were often described as having a "scorpion-like" tail, although most historical illustrations show a cluster of spikes on the end of the tail instead.

When the creature was adopted for D&D, however, Gygax made a major innovation to the mythic creature: he gave it wings. (At least, this is true by the 1E Monster Manual; the original version of the rules apparently doesn't mention the feature). Although this is original to the game, it has become a common trope of manticore pictures since, even outside of D&D, although it's far from universal.

D&D Monsters: Griffons and Hippogriffs

The mythic origins of griffons lie in Ancient Greece, if not earlier - a combination of the king of the beasts and the king of the birds. The specific form of that combination was largely cemented by the late Middle Ages into the one we are currently familiar with, and griffons ('griffin' and 'gryphon' are equally valid spellings) are common features in modern fantasy, especially in RPGs. 

The hippogriff, however, is much more modern; it first appears in a poetic work of fiction written in 1516, where it is described as the offspring of a male griffon and a female horse (which, since griffons were thought to kill and eat horses on sight was intended as something miraculous). Although the existence of one may well imply the other, it's possibly more common than the griffon itself in fantasy fiction, with the most famous modern example being that in the Harry Potter books.

D&D Monsters: Mummies

The concept of the mummy as an undead monster is really a 20th-century invention, beginning with the 1932 horror movie The Mummy. While mummies and immortal Ancient Egyptians had featured in earlier fiction, they were not really in the form we're familiar with now, or that formed the basis for the D&D monster, and still don't date back any further than the mid-19th century. Since their 1932 debut, however, they have appeared in a number of older-style horror films, and become something of a cliche, if not quite as popular as werewolves and vampires.

In D&D, they are mid-powered undead, falling into what I've termed the "wilful corporeal" category, given that they retain sentience and intelligence alongside their physical body. Under that scheme, they would fall somewhere between a wight and vampire in terms of power, but they are quite different from both. The look of a mummy does not, of course, change notably between editions; they are bandage-wrapped mummified corpses, sometimes dressed in funereal finery, but more usually not. Like most D&D undead (except vampires) depictions of females are rare, although not quite to the extent that is true of, say, ghouls or wights.