The Boy Who Couldn't Die — William Sleator

When his best friend is killed in a plane crash, Ken makes a decision: He will never die. He finds a woman who claims she can make him invulnerable to pain and death for the unbelievably cheap price of fifty dollars. And her strange ritual works. Ken can't be burned, beaten up, or even bitten by the sharks he dives among on his spring break in the Caribbean.

Ken can't die, but he can kill. As long as he's awake, he feels in complete control of his life. But at night the dreams take over -- dreams of digging up graves, of knifing strangers ... then of trying to murder someone he loves. And no one can stop him, not even himself.