The Nameless One is a human male who long ago found a way to cease the aging process and become immortal. In addition, any wounds inflicted upon him are magically healed, although they can and do leave scars. He can be killed, but his body heals itself and he comes back to life after dying. However, when he is killed in an especially thorough manner, although he does come back to life, when he awakens he will have lost all his memories, and often developed an entirely different personality from the one he had before. It is implied that he has lived for centuries, if not millenia, and in his travels has befriended and made enemies with hundreds of people, and been a brutal warrior, a passionate lover, a deceitful liar, and even (despite his meaty appearance) a powerful sorcerer. At the point where Planescape: Torment begins, his latest incarnation awakens in a mortuary, having lost his memories yet again. At this point, The Nameless One is so covered in dead flesh in the form of scar tissue that he can use embalming fluid as a substitute for healing potions.
Torment is spent trying to piece together his past and explain why he can not be killed. His age is unknown, but he is believed to be many thousands of years old and to have had thousands of incarnations.
The Nameless One's origins and early life have been lost in time, although it is known that at some point he committed a grievous crime damning him to an eternity fighting in the Blood War, a never-ending conflict between demons who worship chaos and demons who worship order, each side equally evil. To escape this grim fate he sought the night hag Ravel Puzzlewell, and presented her with a challenge to make him immortal, hoping that if he spent the rest of eternity atoning for his crime, eventually he would be forgiven. Ravel's ritual worked, and as payment The Nameless One offered her a riddle:
What can change the nature of a man?
To test the ritual Ravel murdered him. When he "recovered" he had no memories of his life. He could not remember his name or what had driven him to seek immortality, leaving him in a similar state to the way we find him in today.
At the start of the game, in the mortuary, The Nameless One meets Morte Rictusgrin, a floating skull. Morte is a longtime companion of his, although Morte does not reveal this straight away. Throughout the world The Nameless One continues to meet people whose lives his previous incarnations have affected, some of them, like Dak'kon are available as companions and have played large roles in the life (lives?) of The Nameless One. Not all the characters that have been affected by The Nameless One are important to the game's plot, even some of the most unimportant seeming NPCs have some relation to previous incarnations.
As the game progresses The Nameless One eventually comes face to face with Ravel again, she reveals that she is indeed the one responsible for his immortality. Ravel reveals that she separated him from his mortality, and because she did not destroy it, it must still be intact. She does not know where though, and suggests that he seeks out Trias, a fallen angel. When he attempts to leave Ravel attacks The Nameless One and his party, and though she appears to be defeated, once they leave she gets back up. However, she is soon killed for real by a mysterious entity known as The Transcendent One.
The Nameless One's search for Trias takes him to Curst, a prison town on the border of the Outlands and Carceri. Here he breaks into prison and eventually frees Trias from his chains. Trias denies knowledge of the location of The Nameless One's mortality and sends him to the Pillar of Skulls in Carceri, where people who caused other people to die through telling lies end up in the afterlife. It was here that The Nameless One met Morte hundreds of years ago; out of thanks, Morte followed The Nameless One through dozens of incarnations; unlike The Nameless One, whose immortality is magical, Morte is already dead, and therefore doesn't age. The Namless One learns from the Pillar that he must seek the Fortress of Regrets and that only Trias knows how to access this place.
On return to Curst the town is found under attack by demons. It had slid from the lawful realm of Outlands into the chaotic realm of Carceri, all caused by the chaos unleashed when The Nameless One freed Trias. After a fight with Trias it is eventually revealed that the portal to the Fortress of Regrets is located in the Mortuary in Sigil, the very room that the game started in.
He returns to the mortuary and enters the Fortress of Regrets. There, he learns the terrible price for his Immortality: every time he dies, the life force is drained from a random person in the Planescape, the grand collection of universes, and that person drops dead while The Nameless One comes back to life. All that is left of these "victims" is a vengeful shadow, and hundreds of these shadows infest the Fortress, having waited centuries for the chance to get their revenge on The Nameless One.
After fighting his way through the Fortress, The Nameless One meets three of his past incarnations: one good, one practical, and one paranoid. The good incarnation is revealed to be the original, the man who made the deal with Ravel. Eventually he comes face to face with his mortality, in the form of The Transcendent One, who reveals that he has enjoyed being separated from The Nameless One. He goes on to say that he has been attempting to erase clues to stop The Nameless One from finding out the truth so that The Transcendant One would be a seperate being from him forever.
Should the player chose to do so, a fight ensues during which The Nameless One either kills his mortality or convinces it to rejoin with him. Both paths lead to The Nameless One no longer being immortal, finally allowing him to die.
In the game's ending sequence The Nameless One awakens on the field of battle in the eternal Blood War, belatedly arriving at the fate he was damned to so many years ago. He picks up a weapon and enters the fray, and the game fades to black.
During the final outro, the riddle "What can change the nature of a man?" is repeated for the last time, but no clear answer is given. It might be regret, which allowed The Nameless One to enter The Fortress of Regrets, or belief, belief that The Nameless One can escape his punishment. Or perhaps nothing can truly change the nature of a man, because no matter how hard he tried to change his destiny, The Nameless One joined the forces fighting in the endless Blood War.
In fact, there is probably no one right answer, every incarnation might have it's own version. Because of it's subjective nature, the riddle could have served Ravel as a test of character of different incarnations of The Nameles One.
The Good Incarnation
The good incarnation is the original incarnation of The Nameless One. Despite his good intentions, the crimes he committed were so severe that no amount of repentance would forgive them. In his remorse he sought out Ravel so that she might make him immortal so he could spend an eternity attempting to make up for his crimes. He believes that regret can change the nature of a man.
The Practical Incarnation
The practical incarnation was one of the most powerful incarnations of The Nameless One. He is the one that has seemingly had most impact on The Nameless One achieving his goal. Although seemingly evil and manipulative, all of what he is known to have done was to further his goal of one day becoming mortal again. He is the only known previous incarnation to have successfully entered the Fortress of Regrets, although it is implied he died there when facing his mortality.
The Paranoid Incarnation
The paranoid incarnation is totally insane and extremely cautious. He set many traps in locations important to him. He is known to have killed many people that tried to help him.