The most obviously evil character in the story is Assef. As a child, Assef is bullying and sadistic. He is an avid proponent of Hitler and Nazism. He rapes Hassan and later becomes a Taliban leader. However, Assef is evil from the beginning.
The character who perhaps most obviously becomes evil, albeit not permanently, and not to the extent of Assef, is Amir.
At the beginning of the story Amir is a character who, despite his flaws, we feel pity for. He is selfish and sometimes mean, but these traits seem excusable, or at least explicable, because of his relationship with his father. Amir's father, Baba, is always very critical of Amir, and shows him little love or affection. Amir's bad qualities seem inversely proportional to the love he receives from his father. The less loved he feels, the meaner he becomes.
However, Amir's bad qualities escalate to a point where it is difficult to forgive him for them. The most obvious example is when he doesn't intervene when Hassan is being raped. He sacrifices Hassan so that he can keep the kite from the kite running competition, which he thinks will help him to earn his father's love. Amir says, "Maybe Hassan was the price I had to pay, the lamb I had to slay, to win Baba." Later in the story, Amir also frames Hassan for the theft of the watch and money that he, Amir, receives for his birthday. This leads to Hassan and Ali leaving Baba's home. Here again Amir's actions are selfish and cruel. He deliberately frames Hassan so that he will no longer have to face the shame and guilt he feels every time he sees Hassan.
Amir does, however, become good again by the end of the story. Indeed, the second half of the story is the story of Amir's redemption. He devotes his life to redeeming, as far as possible, the evil that he has been responsible for in the first half of the story.