So we have...
Humans. Stereotypic European humans and then the Rivani which are the "other" more tribal humans. Avvar are the Barbarian sub-set.
Dwarves. We have the Dwarfy dwarves of Orzammar, the Darker Dwarves of Kal-Sharok, the gnome-like/halfling (Dwarf-lite) Surfacers, and the newly mentioned Sea Captain Dwarves in WoT2 from the West.
Elves. We have the High Elves (Solas, Abelas), we have the Wood Elves (Dalish), we have half-Elves (City Elves, think about it). We don't really have Dark Elves, but I'm getting to the Dark in a second.
Beast. We have the Qunari, who are sometimes referred to as Giants and Ox-men. They are kind of a cross between a minotaur race and a lizard (argonian) race. They are the main "other" of the series. The Kossith seem to be the more savage extreme of the trope, but we don't know, they could have been more cultured and magicky (High Elf style) and the Qunari would still not like them. We also have the Fex, who might fill the niche of the primitive Beast race. We've even had werewolves.
Darklings. Darkspawn, duh, provide a re-imagining of the Dark Elf, Dark Human, and Orc trope. They are the corrupted version of each race.
Fae. Spirits, of course, of which we have a lot of varieties. We have ents (Sylvans), dryads (Lady of the Forest), full fae (Cole), were creatures, we even have god-touched mortals (Wynne, Anders, etc). The Elves are even hinted at being a Fae race (their ears point to the Fade, their blood is better for magical blood rites, etc). We even have the Elven Gods.
Personally, I prefer what they are doing. They take the typical races in fantasy and strip them down to their roots. What really is the difference between a High Elf and a Wood Elf? If Elves are mutable, why do they really need sub-races, and not just sub-cultures? What would a new beast-race offer that the Qunari don't? There are a lot of races and cultures already in Thedas, and I'm not entirely sure we always need a new race, when the same thing could be accomplished by introducing a new culture of an existing race or by throwing spirit mutation into the mix (werewolves).