How do the characters in The Crucible die?
In The Crucible, nineteen innocent people are hanged for the supposed crime of witchcraft.
The Crucible begins after the town minister (Reverend Samuel Parris) catches a group of girls (among them his daughter Betty and his niece Abigail) dancing naked in the woods in Salem, Massachusetts. This is a very serious offense; the girls, afraid of what punishment lies in store for them, quickly claim that the reason for their lapse in behavior is that the spirits of some members of the community have possessed them. They state that their wanton behavior is the result of being initiated into witchcraft by these members of their community. The Crucible is the story of what happens when mass hysteria, fomented by jealousies, malice and grudges, is allowed to hold sway over reason.
Not surprisingly, the girls call out the names of those they hold a grudge against. Abigail Williams singles out Elizabeth Proctor as one of the guilty. Elizabeth was Abigail's employer until she fired Abigail for having an affair with her husband, John Proctor. Abigail is motivated by revenge and jealousy. She simply wants Elizabeth to pay for what she did to her and to pay for still being married to John. Although John manages to get one of the girls, Mary Warren, to confess that the girls' fits are just a clever bit of acting, the whole plan to bring to light the truth threatens to expose John's adultery. Although he eventually confesses the truth, the hysteria has gone too far, and the frenzy of paranoia has completely overtaken the community to the point that the truth is eclipsed by calls for immediate judgment.
John Proctor becomes one of the nineteen victims hanged for a crime he did not commit. Another victim, Rebecca Nurse, who is known for her piety, is also hanged. Giles Corey, an elderly man who refuses to answer any questions about his supposed role in the witchcraft accusations, is pressed with heavy stones on his chest until he dies. Both John Proctor and Rebecca Nurse die courageously with their integrity intact; both refuse to confess to a crime they did not commit and both refuse to implicate other innocent members of the community.
For further reading, you might be interested in Enotes' excellent analyses and complete summary of the play. Links are below. Thanks for the question!