Yes, John Proctor is hanged in the play's final scene. On the day of his scheduled execution, John is urged to confess to save himself from hanging. With two children and a pregnant wife, Proctor has plenty of reasons to continue living. He is in his thirties and would likely have a long life ahead of him.
Proctor briefly considers giving a false confession so that he might live. But he realizes that in doing so he would be setting a negative example for his children, and he would lose the respect of people that matter to him. As a Puritan, he would also be concerned that in telling a lie that amounts to renouncing God, he would be eternally damned.
The authorities want John Proctor to confess because they think it would lend the trials more legitimacy. There is growing public renunciation of the trials because pillars of the community stand accused, like Rebecca Nurse, and the admission of spectral evidence is creating significant doubt. However, John Proctor will not allow himself to be used as a political tool of the theocracy, and so he chooses execution over giving a false confession.