"It seems that the fallen are indeed creatures of demonic origin. The old Horadric tale claims they were once powerful servants of the mythical Azmodan. They purportedly aided him in his battle against the Prime Evils, and Diablo later punished them by twisting them into the small, stupid forms they now possess."— Monster summary(src)
Fallen Ones are encountered in the first, second, and third acts. They are always found in large numbers. Deaths of other Fallen may send them running in fear for a few seconds, they outnumber player quickly, especially when assisted by Shamans. The only way to make the Fallen unable to be raised again is to kill them with a Critical Hit.
Fallen Overseers also have the ability to roar, increasing speed and damage of the Fallen Ones, and making them fearless.