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.