Following up on questions raised in the Plug 'n Play Races post, here's my breakdown of potential "new" races, grouped by theme, that could have enough of a deep cultural resonance to become an iconic race in D&D, with close to the same standing as the standard races. Almost all of these races have appeared in one fantasy RPG or another, but not all of them have been diligently promoted as an iconic core D&D race. They're grouped by theme, tied to source.
Ancient/Classical (and Swords & Sorcery)
Exotics: Basically, just humans with one stand-out difference from the norm, not necessarily an ability. For example, the Greeks didn't think women could be warriors, but they imagined a tribe of women warriors (Amazons.) There's no real Amazon "power", other than "ignore stereotype", but some FRPGs add Amazons with an archery bonus. Individual exotic races may not have an iconic stature on their own, but the general concept of playing an otherwise normal human with one stand-out feature is, itself, iconic, and would work in many settings, especially if "exotic" itself were listed as a race, instead of individual examples. Exotic body shapes are rare, but possible, such as Pliny's exotic human tribes like the Blemys and the Monopods. Humans with more than one physical abnormality tend to be treated as monsters (Medusa) rather than potential humans.
Demi-Beasts: Centaurs, Satyrs, Minotaurs, and, by analogy, other creatures with animal features and behavior.Aside from Greek Centaurs and Satyrs, these usually occur alone and may even be unique; they tend to not have their own culture and may even be wild before being tamed and incorporated into human society, like Enkidu.
Intelligent Beasts: Standard animals, but able to think like a human, understand human speech, and possibly also stand upright or use tools. Older tales tend to have human-like intellects in animal bodies without the power of speech; by the 19th century, the trend is towards animals that can walk and talk, but are still obviously animals in shape, as opposed to the bestial but humanoid Demi-Beasts. Older tales also tend to be one-of-a-kind creatures or former humans cursed into animal form; campaigns with a more 19th-century feel can drift towards secret factions of talking, intelligent animals, like in the story "The King of Cats" or in Lovecraft's "Dream-Quest of Unknown Kadath".
Giants: A very specific kind of Exotic that shows up in many, perhaps most, cultures, but which becomes much more common in early Arthurian tales. Like Demi-Beasts, they tend to be loners and semi-wild.
Dwarfs: Unlike Giants, which are big and strong, Dwarfs are small and cunning, but again are still basically Exotic humans rather than a separate race, unless they are the otherworldly sort (see Fae.)
Ogres: Sort of a cross between Giant and Demi-Beast: a brutish, larger-than-normal human.
Merfolk: A variety of Demi-Beast, humans with fish-like features.
Fae: In Arthurian Romance, humans with a touch of the otherworldly about them. Pretty much every Magic-User in an Arthurian campaign would be Fae, but there are also some Exotics with unusual abilities; there's also usually a vulnerability to cold iron. Outside of the Arthurian tales, they get more otherworldly, and come in many varieties (Giant, Ogre, Dwarf/Goblin/household spirit, and others.) However, the varieties don't seem to be treated as separate races per se, but as part of a broader Fae race; the more otherworldly they are, the more they will have weird strictures like compulsive counting of small objects.
Shapeshifters: Includes both the cursed sort (humans forced to spend a fortnight every month in beast form) and the Fae sort, like swan maidens. The Fae variety usually have a cloak or animal skin that they wear to transform, but occasionally come in groups instead of being completely unique.
Elementals: Mostly come from Paracelsus, who wrote about sylphs, undines, salamanders, and gnomes as spirits of the four elements. These could be developed as iconic races, although the gnome as elemental would be a bit different than the gnome as a variety of Fae dwarf. The Elementals are pretty much the only medieval "race" that don't fall into the category of Accursed.
Accursed: Vampires and werewolves could be developed as extreme Exotics, but again do not have a culture of their own. These and the Fae are treated more as demons or half-demons during this period, so in addition to a vulnerability to iron, silver, or both, they are also vulnerable to the sign of the Cross, holy water, and strictures about crossing thresholds or running water. A lot of the cinematic vampire/werewolf lore hasn't developed at this point, and vampires are even described as having new families in other villages after their death, but they return at night to their original village to drain their relatives of life. Thus, their powers are substantially toned down (and mostly absent in daylight,) while their vulnerabilities are played up, compared to modern vampires.
Gargoyles: Actually, these are still just statuary in the medieval period, but grotesque humanoids, with or without wings, but they've built up enough iconic status that you could run them as some variety of Accursed, or if you wanted a less medieval feel, you could just add them as winged Ogres, as The Fantasy Trip sort of did.
Merfolk: These get tweaked a bit from the fairy tale variety; they are usually much smaller than humans, and come in several varieties that reflect human varieties. Look up Jenny Haniver or Sea Monk for some interesting hoaxes based on this conception of mer-people. Because of the presence of the Sea Monk, it's possible that Merfolk in the Late Medieval period aren't regarded as Accursed.
Genies: Essentially, an arabian equivalent to the Fae, coming in multiple varieties and regional names (Djinn, Ifrit, Peri, Deev,) but still more or less one unified race. Genies seem to get bound by Magic-Users rather than turned by Clerics, but could otherwise be handled as the Fae.
Ghouls: Not necessarily undead, but more like Accursed corpse-eaters. Lovecraft's ghouls are a good model, but enough zombie/walking dead movies have permeated the general cultural consciousness that a Ghoul race (similar to what we see in GURPS Fantasy Folk, maybe) could be iconic enough.
I'll probably have more to say about what this all means in a future post.