The high fantasy setting for the Dragon Age franchise features a predominantly human world in which humans are not only the most numerous but also tend to be the most powerful and dominant race. It wasn't always that way, however. In the earliest recorded Thedosian history, elves and dwarves were the center of the world's cultural evolution. As humanity began to spread across the continent, their assertion wrought havoc on the already collapsing elven culture as the dwarves began to withdraw even further underground.
If the Chantry's recollections of history are true, humanity's hubris was to blame for the creation of Darkspawn, a fifth humanoid race that corrupted everything in its path. Since the Darkspawn are created rather than born, it is difficult to determine if they are actually their own race or simply a corrupted collection of the other races, tainted and driven to wipe out all the others.
Elves
The elves once dominated Thedas, with the reach of their empire, Elvhenan, spanning from Arlathan to Ferelden and westward beyond Orlais. When tragedy struck, the elven culture diminished, as many of them were rounded up and enslaved by the magisters of Tevinter. In time, they were freed, but they had already begun to lose much of their history. Eventually, they divided into two factions: the Dalish -- those who believed they held true to their ancestors, and City Elves -- those who took up residence in the alienages of human cities.
Elves are capable of playing all classes, though the chosen class in Origins determined the player character's origination. Warriors, rangers and rogues could come from the alienage or a Dalish tribe, while mages originated from the Circle of Magi. They received an automatic +2 Willpower and +2 Magic, and in Inquisition they were given a +25% boost to their ranged defenses, including magical projectiles.
Dwarves
The dwarves once ruled a vast, underground empire stretching from one end of Thedas to the other. When the Darkspawn emerged, they cut many of the dwarven thaigs off from each other until only Orzammar remained. By default, Orzammar became the center of dwarven culture and enterprise. Shorter than the other races of Thedas, dwarves tend to be stockier in their build, their bodies designed for battle and hard labor. They dominate trade, being the primary miners of the continent's most sought-after element: lyrium.
Dwarves are the only one of the four races in Thedas who have no access to the Fade and therefore cannot use magic. Whether this results from their constant exposure to lyrium or some other unknown trait remains unknown. They received +1 Dexterity, +1 Strength and +2 Constitution with 10% magical resistance in Origins, while in Inquisition they had 25% magical resistance.
Qunari
There was a Qunari companion in the Warden's party in Origins, and plenty of the horned men antagonized Kirkwall in the second game, but the Qunari did not become a playable race until Dragon Age: Inquisition. Qunari is an umbrella term used to describe all those who follow the Qun, but it is also how the other races tend to identify the giant, white-haired horned men who have been warring with the humans of Tevinter since the Blessed Age.
They have strict moral views and laws regarding magic, tending to sew shut the lips of their mages to protect themselves and others from demons, and have unspoken designs to conquer all of Thedas in the name of the Qun. Qunari Inquisitors were granted a 10% physical damage resistance in Inquisition.
Humans
As the most predominant race in Thedas, humanity might almost be considered a threat were it not for their inability to unite under a single cause. Even amidst the most tragic circumstances, pulling humans together under one banner has proven almost impossible, generally resulting in a final rally at the very last minute. What is known as humanity in the Dragon Age all descended from tribes like the Alamarri, Neromenians and Yothandi, resulting in a variety of different viewpoints, styles and cultures. Though not all humans subscribe to the Chantry's belief system, the religion following the teachings of Andraste tends to be one of the single most unifying factors of broader humanity.
With the option of playing all three classes, human versatility has made them great warriors, dangerous mages and cunning rogues. All humans are granted a bonus ability point at the start of a new game.