Answer:
In Robert Louis Stevenson's novel, as well as in most of the subsequent adaptations of the story, the person known as both Henry Jekyll and Edward Hyde kills himself. In the case of the novel, he poisons himself just as Poole and Utterson break into his laboratory.
In adaptations of it, however, he sometimes employs other methods of suicide; for example, in the ever-popular Broadway show, Jekyll & Hyde: the Musical, Dr. Jekyll throws himself upon Utterson's sword.