The first rank of the iconic race types are the Exotics, which are pretty much just humans with an unusual twist. There are basically three subtypes of Exotics, based on culture, talent, or physical appearance.
Exotic Cultures behave differently than the "norm", but have no real mechanical difference. For the most part, you should just allow players to define their own cultures, if they wish, since it's based on pure roleplaying. "I come from a forest barbarian tribe that lives in the branches of trees!"
Exotic Cultures bleed into Exotic Talents, which do have some minor mechanical benefit. As I mentioned previously, Amazons are either an Exotic Culture (warrior women, no better or worse than other warriors, but unusual in that they are women going against stereotype) or they are Exotic Talents (bonus to Archery, above and beyond what an experienced archer of either gender would get.) I, personally, don't see the need to make every race mechanically better in some way than the norm, but this is the current trend. So, the Amazons are better archers, the Vikings get seafaring skills, Mongols get riding bonuses. An optional approach would be to treat each background as a broad binary skill; yes, you can use a bow, because you're an Amazon, but you don't get a bonus above and beyond what other trained archers get. You also get any other skill that seems relevant to your culture, and might be able to do unusual things normal archers can't, like split move and fire while on foot, using either bow or javelin. Vikings would automatically know how to swim or row a longship, unstep the mast, hoist up sails.
Exotic Abnormals are those that appear physically different than a normal human, but for the most part can be treated as human. Cosmetic differences (blue skin) have no overall benefit, but might be an advantage in certain situations, and a disadvantage in others. Perhaps blue-skinned humans who live in the mountains get a bonus to surprise when attacking from above on a clear day, because they blend into the sky? Other physical differences, like extra arms, are more freakish, but provide a definite benefit. The iconic example of an Exotic Abnormal is a Giant, which has a height advantage and should be treated as stronger than an ordinary human.
Exotic Abnormals start to shade into Demi-Beasts, even if their abnormalities aren't strictly animal features. Those with two or more abnormal features or an extreme benefit are generally considered monstrous and not playable, unless the GM and other players are OK with someone playing a monster. A single abnormality that seems as much a drawback as a benefit might make more sense.
The problem with Exotics is that you can actually find several varieties in classical mythology, legend, and fairy tales, but few have them are commonly known. For example, there were a number of strange races believed to exist in distant lands, according to Pliny and later medieval map makers. You have Monopods, who only have one foot (C S Lewis later used these in the Narnia books as Dufflepuds.) You have Blemys, who have faces in their chest and no heads. We don't generally have an idea of how these should behave, culturally, unless someone is a fan of a particular author's interpretation. As a result, few of them could stand alone as an iconic race, with the exception of Amazons, Berserkers, and Giants. We have preconceptions of each of these: Amazons kill or enslave men, Berserkers go into a battle frenzy and seem to live for conflict, Giants are kind of loners and a touch on the brutish side, with some actually being cannibals.
(Dwarves are a special case, because Tolkien and Disney have given us some really strong images of dwarves that have escaped the bonds of their original creators and merged with our collective unconsciousness. Also, the Greek myth of the immortal Hyperboreans have sort of been absorbed into our concept of Elves.)
So, you really can only squeeze about five iconic races out of the Exotics... but you could also include general rules for making new Exotics in a game product, allowing players to just roll their own as needed. A custom-made Exotic is not itself iconic; we don't have any preconceptions of how Monopods behave, or blue-skinned humans, so they would not make good additions to a generic fantasy game book except as sketchy examples. They work better as rare travelers from an unknown land, immersed in a setting defined by other, more iconic races. They could even be unique, the result of magical accident or strange prophecy. The reason they work better is because we can't simply define the default behavior for that race as "whatever that player does". Once a particular group has played a while with an Exotic character in their midst, the GM and players may develop enough of a concept of what that race is like that they could play a few sessions in the homelands of that race.