Reincarnation, or rebirth, is the process by which a soul is born again, either through the Pattern or the Dark One.
Rebirth through the Pattern[]
Rebirth occurs whenever a soul is reborn into another body, almost always to carry out a specific task. As the Ages pass by the Wheel will often spin out people several times.
There is one case of prophesied reincarnation: the Karaethon Cycle. It tells that one day, Lews Therin Telamon, the Dragon, would be reincarnated as the Dragon Reborn. However, unlike many other souls the reincarnation of the Dragon is to occur only once in the Pattern per Age.
Heroes are another example of souls that are constantly reborn to a specific purpose. The heroes dwell within Tel'aran'rhiod until the Wheel spins them back into the Pattern, but they can also be called directly into the waking world when the Horn of Valere is sounded.
There is also debate of reincarnation in the case of Mat Cauthon. Since he had the holes in his memory filled out, he seems to have the lives of many men in his head. These are generally regarded to be either his past lives, or men who came to the The Finn, but the truth is not confirmed, and the memories could very well be of his past lives.
According to Semirhage, in the Age of Legends this concept was well studied. In cases of insanity, when people heard voices in their heads, very rarely the voice would turn out to be that of the person's past life. Reintegration with such people was almost impossible.
Rebirth through the Dark One[]
In addition to rebirth by being spun out of the Wheel, a less natural way is possible, which is rebirth by having one's soul placed into another body by the Dark One, giving meaning to his alternate name, the Lord of the grave. This has been done with several of the Forsaken, most notably Moridin. This is reportedly rare and seems restricted to those Forsaken who are most loyal or have accomplished the most, though the Dark One has made it quite clear that a third chance will not be given to those who die in their second body, no matter what their achievements. Those who undergo this type of rebirth retain their own memories and personalities. The Dark One also seems to have a kind of twisted humor regarding rebirth, as is obvious when Balthamel was reincarnated into a woman's body.
Although the Dark One's reach beyond life is great, it has been stated that even he cannot reclaim a soul that was killed with balefire.