To examine the concept of denial in The Crucible, once could look at a few characters and their situations.
Abigail Williams is in denial about the truth of her relationship with John Proctor. He is a married man who succumbed to lust and had a brief affair with an inexperienced teenager. He loves his wife and family and intends to rebuild his marriage because he knows that what he did was a horrendous mistake. Abigail is unable to see that in John's eyes, the relationship they had was primarily sexual and without a future. She refuses to recognize that he is a man who will not throw away his domestic situation over a mistake: having sex with her.
John Proctor also suffers, for a time, from denial. Although his wife correctly informs him that Abigail Williams is an ongoing threat to their marriage and her very life, John refuses to recognize the truth in what Elizabeth observes. John believes that since the affair is over in his mind, it must be over in Abigail's, as well, though she gives him plenty of signals that she intends to continue her pursuit of him. It is only in Act III that John opens his eyes to the truth of Abigail's desperation to have him.
Reverend Samuel Parris is also in denial for a great portion of the play. Although it is clear that his slave, niece, and daughter are dabbling in witchcraft, he believes that he can handle the situation and emerge with his life and career intact. Inviting Reverend John Hale to Salem may seem to him a career-enhancing move that shows him to be an effective spiritual leader, but it ends up backfiring as the trials gain momentum and the remnants of his congregation turn against him.
Reverend John Hale also spends a portion of the play in denial. He is caught up in his own reputation as a witch hunter and comes into Salem overeager to show off his skills. Though there are many indications to the contrary, he clings to his belief in the presence of witches in Salem until Act III.