The Forsaken was the name given to Aes Sedai who went over to the Shadow in the War of the Shadow at the end of the Age of Legends (Robert Jordan Question of the Week, Week 12 2004). They prefer to call themselves "The Chosen". They went to Shayol Ghul to give their oaths to the Dark One. They each had their own reasons reasons for pledging allegiance to the Shadow, but the promise of immortality was certainly a major factor for each of them. Originally, there were many more Forsaken than just the thirteen. Some were killed by the Dark One because he suspected they weren't trustworthy enough. Others were killed by competing Forsaken. The Dark One actually encouraged them to kill each other off, because he only wanted the strongest and most skilled to serve him. Only one of them was promised to become Nae'blis - and that one would be granted to rule the world from a position only one step below the Great Lord himself. Turnover in the upper ranks was high, but several of the thirteen that were trapped at Shayol Ghul were always among the ones at the top. Many of the original Forsaken were much weaker in the One Power. Today they would probably have been considered Dreadlords, but at that time they were all titled Forsaken/Chosen.
After their oaths were given they received a mark by the Dark One that gives them a measure of control over Shadowspawn. It also enabled him to find them at any time, such that they cannot hide from the Dark One (ToM, Ch. 5). This mark is different from the mark that Alviarin received from Shaidar Haran. Her mark gives her away as protected by the Dark Lord to all Shadowspawn, but she is not able to control them. The male Forsaken were provided with a filter that shielded them from the taint. After the Strike at Shayol Ghul and the sealing of the Bore, the Forsaken left behind were no longer protected by the Great Lord. The men went mad from the taint and the females perished because of the Breaking of the World.
Some of the Forsaken were given the ability to channel the True Power, which emanates from the Dark One himself. The True Power, in contrast to the One Power, can be drawn by males and females alike. Apparently, only twenty nine of the Forsaken have ever been granted the ability to use the True Power (ACoS, Ch. 25) during the last three thousand years or so. After Moridin was named Nae'blis, only he continued to have access to the True Power. It should be noted that this comes with a very high price. The Power that comes from The Lord of the Grave eventually makes the wielder go crazy. Moridin's eyes fill with saa, visible to those around him.
Among the thirteen, Ishamael was free to roam the world in cycles. Whilst back in his prison, he was still aware of what was going on in the world, as were Aginor and Balthamel (Robert Jordan Question of the Week, Week 14 2004). Those who spent three thousand years in dreamless sleep woke up to a world where Common Tongue was spoken, as opposed to the Old Tongue that was spoken when they were trapped. Adapting to these changes was easier than it may seem, because the Common Tongue is actually derived from the more sophisticated Old Tongue.
The title "Lord of the Grave" has proven to be an accurate one. Though several of the thirteen has perished since they were freed from their prison, a number of them were recycled into new bodies. They were also given new names - by their master himself this time. However, his ability to master death is restricted when it comes to balefire. That is because balefire burns the souls away from the Great Pattern even before they were balefired. There's a time-limit that even the Lord of the Grave cannot bridge (Robert Jordan Question of the Week, Week 3 2004). He has to catch the souls of the deceased within a limited timeframe. Robert Jordan has also confirmed that Sammael won't be resurrected (CNN chat transcript, 12 December 2000):..."Mashadar killed Sammael. Sammael is toast!". That makes sense, because Mashadar is the evil fog that feeds on souls. Apparently the Dark One cannot make Mashadar throw up what has been chewed down!
List of Forsaken
Believed to be the most powerful among the Forsaken. He was only partially trapped by the seals on the Bore. Thus, he was thrown out of his prison and drawn back again on a regular cycle. He is a frequent user of the True Power and he is believed to be more than half mad. As Ba'alzamon he was killed by Rand in Tear (TDR, Ch. 55). He has been given a body of a young man, and now calls himself Moridin (which means "death"). He has been named Nae'blis by the Dark One. Alive and at large.
Also known as the Asha'man Corlan Dashiva and/or Osan'gar. He was believed to be the second most powerful of the male Forsaken. During the Age of Legends he created the Shadowspawn. At the closing of the Bore he was caught just beneath the surface. Because of this, he was one of the first to awaken. He was killed by drawing too much of the One Power (TEotW, Ch. 51). After that the Dark One gave him a new body and renamed him "Osan'gar". Believed dead (vaporized by Elza at the end of Winter's Heart).
During the Age of legends, he didn't manage to earn his third name. He was killed by the last of the Nym at the Eye of the World (TEotW, Ch. 50). He was recycled into the body of an attractive woman, and the Dark One gave him the name Aran'gar. He was pretending to be Delana's secretary (Halima) as well acting as Egwene's masseuse. Both Aran'gar and Delana fled the camp of the rebel Aes Sedai after being exposed. Accidentally balefired by Rand al'Thor.
Also known as Lord Brend of Illian. During his time in Illian, he got hold of a stasis box that contained some useful stuff. He was killed by Mashadar in Shadar Logoth at the end of A Crown of Swords. Someone using his face has been ordering Shadowspawn, but Robert Jordan confirmed he was dead and gone (This passage needs a reference).
Current location unknown, though he claims to be massing an army and to be ready for war. Alive and at large.
Also known as Jasin Natael (Bard of the Dragon Reborn). Lanfear shielded him at Rhuidean (TSR, Ch. 58), and thus he became the tutor to Rand. He was killed by an unknown culprit (TFoH, Ch. 56), but afterwards no body was found. There is much debate as to who the perpetrator is. The Dark One has stated Asmodean as one of those that will not be given a second chance:... "WHO BETRAYS ME SHALL DIE THE FINAL DEATH. ASMODEAN, TWISTED BY HIS WEAKNESS. RAHVIN, DEAD IN HIS PRIDE." (LoC, Prologue). Dead and gone.
Alive but trapped in a cour'souvra. Also known as Selene, Keille or Silvie. She is also known to have taken the appearance of Else Grinwell (in The Dragon Reborn). Thus it's highly likely that she knows the weave required to make herself appear weaker in the One Power than she actually is. The existence of such a weave has been confirmed by Robert Jordan (This passage needs a reference). She was the most powerful of the female Forsaken. She has a great Talent for Dreamwalking, second only to Moghedien (among the Forsaken, at least). Tackled by Moiraine (TFoH, Ch. 52), they both toppled through the Eelfinn gateway ter'angreal. She was given a new body, and now she goes by the name Cyndane. For some unknown reason, she's somewhat weaker in the One Power than she was as Lanfear (WH, Ch. 35), though still stronger than Graendal.
Also known as Lady Basene, an isolated Domani noble. During the Age of Legends she was a psychiatrist and an ascetic. After turning to the Shadow she changed her manner completely. Some theorize that she could have been turned evil due to a circle of thirteen. She uses Compulsion on a regular basis. It's widely hinted that she may have killed Asmodean. Taken by Shaidar Haran as punishment for her failings.
Caught by Rand and company (KoD, Ch. 27). Also known as Anath. She was a brilliant healer of the body during the Age of Legends. She hates Lanfear passionately, and wears black as opposed to white (which is Lanfear's style). She is as tall as most men. She was killed by Rand al'Thor, using the True Power to weave balefire.
She is the most talented of all Forsaken within the realm of Tel'aran'rhiod. She was about equally matched in the One Power as Nynaeve. Alive but trapped in a cour'souvra.