Darkspawn

According to the Chantry, they were created when the Magisters Sidereal of the Tevinter Imperium opened a portal into the Golden City, tainting the realm of the Maker with their corruption and returning as the first darkspawn, their evil transfiguring them into the monsters they became. The taint they carried infected others, turning them into darkspawn as well.

With their increased numbers, the first darkspawn went underground and dug deeper and deeper into the earth until they found the resting place of the Old God Dumat, where he had been imprisoned. Freed from his prison and warped by the taint the darkspawn bore, Dumat became the first of the Archdemons and led the darkspawn to lay waste to the world in what would become known as the First Blight.

Views from other cultures
Other cultures view the Blights in different lights than those of the Ferelden Humans

Dwarves
The dwarves give little credit to Chantry beliefs, but they themselves have no known origin story for the darkspawn. As far as the dwarves are concerned, the darkspawn simply appeared underground with some Shapers hypothesizing that there is a queen broodmother-the first mother. The darkspawn hordes first invaded the Deep Roads ended up crippling the dwarven empire, leaving only Orzammar and Kal-Sharok, the latter was discovered only recently that it survived.

Tevinter
Magisters deny their involvement in starting the Blight. They claim the darkspawn have always existed and the magisters have no connection to them.

History
With the fall of the Golden City and the beginning of the First Blight in -395 Ancient (800 TE), a dark age descended onto Thedas as the darkspawn rampaged across the continent, destroying everything in their path. The Tevinter Imperium suffered greatly, as it weakened greatly and fracturing under the strain of the invasion, while the subterranean empire of the dwarves was laid waste, with only their four major kingdoms Orzammar, Gundaar, Hormak and Kal-Sharok surviving. After nearly a century of hopeless, unending war, the Order of the Grey Wardens was established at Weisshaupt Fortress in -305 Ancient (890 TE), and proved instrumental in the defeat of the Archdemon Dumat at the Battle of the Silent Plains. The darkspawn invasion had been beaten, but the darkspawn would retreat underground to rebuild and recover.

Over the centuries, four more Blights would occur, the latest occurring in 9:30 Dragon. Each time, the Blight would be stopped with heavy losses, with the darkspawn destroying entire cities or even kingdoms before being beaten back by the nations of Thedas and the Grey Wardens. With the exception of Anderfels, darkspawn appearances on the surface most frequently promote fears of a Blight, however this does not occur until an Archdemon is awakened by the darkspawn. Without the Archdemon leading them, darkspawn hordes are much smaller and less effective in the raids they often launch, but are still dangerous. However that's not the case in the underground, as the dwarves are constantly fighting a losing battle against the darkspawn for more than a millennium. This resulted in the underground of Thedas being entirely controlled by the darkspawn with the exception of what remains of the kingdoms of Orzammar and Kal-Sharok, but some thaigs have been recently reclaimed.