Corey, in Act I, mentions to Rev Hale that his wife Martha reads strange books and that he can't say his prayers one night while she is reading.  Once she stops, he can pray again.  He just wants an explanation for why his third wife, Martha reads so many books.

Rev Parris, in Act I, is interested in protecting his job and his reputation.  He does not feel accepted by the congregation in Salem, and when Betty gets sick, and the Doctor can't help her, he sends for Rev. Hale to help her.  He is really helping himself.  

The Crucible begins with two sick children, Betty Parris and Ruth Putnam. Neither will "wake" from their seemingly comatose state. As the Act unfolds, and answers are sought, two important ideas are revealed. First, the girls have been discovered dancing in the forest, a formidable sin. Second, the girls may have been participating in witchcraft, a deadly sin. As the girls are questioned, and as more characters are involved, the situation becomes more severe. When the girls are left alone in Betty Parris room, they begin conspiring to hide the worst offence - the witchcraft. When the questions become too hard to answer, a new plan emerges -- blame someone else. Abby blames Tituba, who blames Goody Good and Goody Osbourne. Then the other girls join in, calling names and passing the blame. Throughout the development of the Act, a single motivation dominates -- self-preservation. No one wants to bear the blame. Parris doesn't want to bear the consequences for such sin being in his house. Abigail doesn't want to bear the consequences of conjuring spirits to kill Goody Proctor. The Putnam's don't want to bear the consequences of conjuring the spirits of their departed children. Tituba doesn't want to bear the consequences of teaching the children to conjure. Everyone is looking to save themselves the consequence for their own actions, so everyone is looking for someone else to blame.

Abigail Williams persists with her lies for a number of reasons. First and foremost, she wants to save her own skin. It was Abby, along with the other girls, who was getting up to all kinds of witchy mischief in the forest that night. Falsely accusing others of witchcraft is a useful way of taking the spotlight off her weird cavortings.

Abby also loves the immense power that the witch-craze gives her, something that she's never had before. An accusation of witchcraft from her, no matter how ridiculous, is tantamount to a death sentence, and Abby loves having the power of life and death over others, especially the people who've done her wrong.

And that leads us on to the third main reason for Abby's lying: she wants revenge on the Proctors. Abby and John had a brief, tempestuous affair. But after John's wife Elizabeth found out about it, John dumped Abby and she was forced to leave the Proctor household, where she'd been working as a maidservant. Ever since then, Abby has been boiling with rage, determined to get payback for what she sees as the Proctors' shabby treatment of her. And what better to do that than to make false accusations of witchcraft against them, safe in the knowledge that she'll almost certainly be believed.

In Act III, scene i of The Crucible, Abigail accuses Mary of lying in her testimony because she wants to keep her own ruse going.  She still hopes that somehow, these false accusations of witchcraft will help her to win John Proctor in the end.  She also likes the sense of power she gets from the attention she is receiving in court - the judges hang on her every word, and the other girls follow her lead.

Mary, prior to testifying in court, had been one of those girls following Abigail's lead, but once away from that "mob mentality" and confronted by John Proctor, she comes to court to admit she has been pretending - that she has really not seen any spirits; it's all been an act.  She hopes to clear Goody Proctor's name with this testimony, but Abigail has other ideas. 

When Abigail returns to court, Judge Danforth confronts her, saying:

"Your friend Mary Warren has given us a deposition. In which she swears that she never saw familiar spirits, apparitions, nor any manifest of the Devil. She claims as well, that none of you have seen these things either.... Abigail Williams, rise. Is there any truth in this?"

Abigail vehemently denies the charge and goes on to also accuse Mary of lying about the poppet (which Mary had explained to the judge was her own and that Abigail had seen her sewing it in court).  Abigail, still trying to make the court believe the injury she suffered in her side was due to the "voodoo technique" used by Goody Proctor, claims that when she worked for the Proctors, "Goody Proctor always kept poppets." 

Soon, Judge Hathorne brings the attention back to Mary, saying:

"You say you never saw no spirits, Mary, were never threatened or afflicted by any manifest of the Devil or the Devil’s agents? ... And yet, when people accused of witchery confronted you in court, you would faint, saying their spirits came out of their bodies and choked you."

When Mary admits, "That were pretense, sir," Hathorne asks her to "pretend to faint now" to prove what she is saying.  However, Mary cannot faint at their request, and explains:

"I used to faint because… I… I thought I saw spirits.... But I did not, your Honor.… I heard the other girls screaming, and you, your Honor, you seemed to believe them and I… It were only sport in the beginning, sir, but then the whole world cried spirits, spirits, and I… I promise you, Mister Danforth, I only thought I saw them but I did not."

At this, Danforth calls upon Abigail Williams again to "search (her)heart" to see if it is possible that "the spirits (she has) seen are illusion only."  Abigail angrily retorts to the judge:

"I have been hurt, Mister Danforth; I have seen my blood runnin’ out! I have been near to murdered every day because I done my duty pointing out the Devil’s people—and this is my reward? To be mistrusted, denied, questioned like a…  Let you beware, Mister Danforth—think you to be so mighty that the power of Hell may not turn your wits?!—beware of it!"

After this, she begins her insidious act, shivering and looking at Mary, saying that "a wind, a cold wind has come," and accusing Mary of "send(ing) this shadow on (her)."

This act is only brought to an end by Proctor's accusation that Abigail is "a whore," and the focus after this shifts to the alleged illicit relationship the two have shared.

Betty Parris's actions seem mostly to be motivated by fear.  In Act One, she only wakes up long enough to accuse Abigail of drinking "a charm to kill Goody Proctor," and then again at the very end of the scene to accuse townsfolk of witchcraft.  She seems to fear that she and the other girls will be in a great deal of trouble for the things they did in the forest, and when she has another outlet for that anxiety and fear, she uses it.  The stage direction says that she "call[s] out hysterically and with great relief" when she accuses them.  This opportunity to scapegoat other women eases her fear and worry.

Mrs. Putnam is motivated by her desire to find out why she has lost seven out of eight babies.  She admits that she sent her daughter to Tituba in order to conjure their spirits and find out what killed them.  When she sees her daughter "turning strange" and "shrivel[ing] like a sucking mouth were pullin' on her life too," she panics and is willing to attempt anything to save her and find the cause of her terrible misfortune.

Mary Warren is motivated by concern for herself.  She doesn't want to tell the truth about Abigail and the other girls lying because she is afraid that they will accuse her too.  Though Proctor succeeds in getting her to testify against the others in Act Three, she ultimately turns on him when Abigail accuses her of sending out her spirit. 

Giles Corey is motivated by his guilt for accidentally implicating his wife as a witch.  In Act One, he asked Mr. Hale what to make of the fact that she reads all the time and that she hides her books from him.  Further, he mentioned that he was unable to pray when she was in the house but when she left he could pray again.  Later, in Act Three, his guilt compels him to storm the court with his evidence against Thomas Putnam in order to prove her innocence.

Rebecca Nurse is motivated by genuine concern and love.  She is wise and understanding.  She says, "A child's spirit is like a child, you can never catch it by running after it; you must stand still, and, for love, it will soon itself come back."  She seems to intuitively understand that the children are fine and that, with time and love, they will be well.  Further, she thinks it is dangerous to seek "loose spirits" and would rather they look to themselves for the cause of any of the town's problems. 

Tituba is largely motivated by her fear of being punished.  When Abigail first accuses her of witchcraft, Reverend Parris threatens to "whip [her] to [her] death" and Mr. Putnam calls for her to "be taken and hanged."  Immediately after these threats, she confesses to being coerced by the Devil to work for him.

Tituba is also probably motivated by a desire to please Mr. Hale, the only person in this community who has ever treated her gently.  He "takes her hand," surprising her when he speaks "kindly" to her.  He tells her that she's "God's instrument" put into their hands to help them root out the evil in Salem; he says that she has a special purpose, and she likely wants to give him what he wants: a confession.

Finally, Tituba probably feels that this is an opportunity to scare Parris, a man who is obviously quite willing to abuse her.  She says that the Devil wanted her to kill Parris, that he's "no goodly man, [that he's a] mean man and no gentle man," and that the Devil bid Tituba to cut Parris's throat.  Such a threat might make him think twice before he beats her again.

The first and most obvious, is the Reverend Samuel Parris, the village priest. Reverend Parris used to be a merchant and had a history of inviting derision wherever he went. When he arrived in Salem him brought with him not only his slave, Tituba, from Barbados, his daughter, Betty and niece, Abigail Williams, but also a long history of paranoia.

It did not take the Reverend long to feel that he was being persecuted by members of his congregation. He was terrified about being ousted from his position and had a need to protect his reputation at all costs. He felt that there was a 'faction' led specifically by John Proctor, Rebecca Nurse and Giles Corey whose sole purpose was to rid Salem of him, so when rumours of witchcraft were traced to his household because of the actions of his slave, daughter and niece, he made every attempt to clear his name.

The Reverend was so anxious about this that he constantly meddled in the court's affairs during the witch trials, to such an extent that he irritated Judge Danforth who, out of contempt for him, commanded him to shut up at one point. The Reverend's desperate attempts to retain his reputation and his position were, however, an exercise in futility. When the trials ended he was voted out of his post and left Salem, never to be seen or heard of again.

Another villager who was keen to protect his reputation was Thomas Putnam, the son of the wealthiest resident in the village. He had many grievances and huge resentment towards many in the village. He had consistently tried to manipulate affairs in the village to improve his reputation and status, with limited success. His failures in this regard made him a deeply embittered man, for, as Arthur Miller states: 

... he regarded himself as the intellectual superior of most of the people around him.

and

Thomas Putnam felt that his own name and the honor of his family had been smirched by the village, and he meant to right matters however he could.

It is primarily for these reasons and his greed for others property that we find Thomas Putnam's names on most of the indictments against others for witchcraft. The trials offered him an opportunity to, as he believed, vindicate his good name and also, to enrich himself and gain greater status and authority.

Another individual intent on, not only to enhance his reputation but to assert it in whichever way he possibly could, was the mean and unscrupulously arrogant and stubborn head of proceedings during the trials, Deputy Governor Danforth. The judge was much aware of his reputation and consistently reminded witnesses and accused of his status and power, lest they forget. He, for example asks Francis Nurse the following during trial:

And do you know that near to four hundred are in the jails from Marblehead to Lynn, and upon my signature?

And seventy-two condemned to hang by that signature?

The judge obviously relishes his reputation as a no-nonsense dispenser of justice. No one dare challenge his authority, for they will face his most severe retribution. He is a commanding and dictatorial force throughout the trial, stamping his personality, authority and reputation on all the proceedings.

Finally, one has to mention the ill-fated John Proctor, our chief protagonist. His reputation was important to him for all the right reasons. John took a strong moral stance in defending his name once he had given his persecutors what they wanted: a false confession. He even went as far as signing such confession but when asked to hand it over, he balked. He would not have his name tarnished any further. His confession would be displayed for everyone to see. Since he was a respected man in the village, it would encourage others to follow his example. When asked why he refuses to hand over his confession, John in agony for what he had done, passionately cries out:

Because it is my name! Because I cannot have another in my life! Because I lie and sign myself to lies! Because I am not worth the dust on the feet of them that hang! How may I live without my name? I have given you my soul; leave me my name!

And in his final words before he is led to the scaffold, he tells Elizabeth:

Give them no tear! Tears pleasure them! Show honor now, show a stony heart and sink them with it!

Betty and Ruth both suffer from severe fright as a result of being caught in the woods dancing, chanting, and casting spells with Tituba and the other girls. 

For one thing, the woods are considered evil and the dwelling place of the devil and his followers.  We all know this is the only place the girls could carry out their harmless activities in private, but it is their bad luck that Reverend Parris happened along.

Also, Parris is her father.  He is already on the outside of the community's heart by making unreasonable demands and requests of these people.  She recognizes that her behavior would give the community one more reason to kick him to the curb and get themselves another reverend.

So, Betty's problem is that she fears her father's wrath as well as the community's judgement for her actions.  Therefore, she is "frozen" and unable to wake up for a time being which is a defense mechanism employed by the girl's subconcious.

One of the best examples of a character from Miller's work who stuck with morals and convictions and bucked the social conformity that was driving Salem would be Giles Corey.  Miller depicts Corey as a voice of dissent throughout the narrative.  He constantly voices his own opinion as opposed to acquiescing to what Salem society demands. The best example of this would be his unwilligness to name his informant, recognizing that divulging that information would put the informant at risk.  His death represents the strength of individual convictions in the face of community based oppression.

Rebecca Nurse might be another example of someone who stayed true to her convictions and went against the community.  From the start of the drama, she repels the ideat that there is witchcraft in the community.  Rather, she claims that it is an example of kids and adolescents simply being kids and adolescents.  She never surrender this point of view. Her sadness when she realizes that Proctor has confessed is a note of shame on him, something he feels and recognizes in her own truth to her convictions.  The look of abject embarassment and shame in his condition at this point reflects that she remained true to her morals and went against the community, paying the ultimate price for it.

John Proctor's strength of character at the end of the drama is an example of an individual who sticks with the commitment behind his "name" and does not give in to what the community wishes.  Proctor does for an instant give in.  He is able to give a confession in order to live.  Yet, he recognizes that there is an inherent danger in this.  Thus, he rejects it in the name of his "name."  The fact that he sticks with his commitment in the face of certain death represents how he goes against the community in the idea that he must represent that which is true and honest in a world that does not.

In act three, John Proctor attempts to undermine Abigail Williams's authority and influence over the court by publicly confessing to lechery. In the Puritan community of Salem, such a confession is damning and will permanently ruin John's reputation and name. However, John Proctor feels obligated to admit that he carried on an affair with Abigail in the hope of putting an end to the corrupt witch trials, which have claimed the lives of numerous innocent citizens.

Tragically, Elizabeth Proctor is questioned about her husband's infidelity and lies to Deputy Governor Danforth in an attempt to preserve and save her husband's reputation. Before lying to the court officials, Elizabeth Proctor is not aware that her husband has already confessed to having an affair with Abigail Williams and has sworn that she, Elizabeth, is an honest woman. Ironically, Elizabeth's testimony damns her husband, who is arrested for attempting to undermine the court. Overall, Elizabeth lies to Danforth about her husband's affair in an attempt to save John's reputation. She is fully aware that such a confession will ruin John's name throughout the town and attempts to protect him from public shame by lying on his behalf.

Tituba seems motivated by fear. Before Tituba's "confession" that she worked with the Devil, Putnam demands Tituba be hanged, and Parris threatens to "whip [her] to [her] death." Tituba tells Putnam and Parris what they want to hear to escape these fates. 

Mrs. Putnam, on the other hand, seems motivated by pain.  Seven of her eight children have died while they were very young, and Mrs. Putnam is desperate to find a reason for why this has happened. She sends her living daughter, Ruth, to conjure the spirits of the dead children in order to find out what happened to them.

Abigail seems motivated by greed and revenge. Her uncle confronts her with the rumors about her reputation in the village, and Abigail seems anxious to reestablish her well-regarded character and make the village pay. Abigail also wants John Proctor, her former lover, all to herself. She also wants to exact revenge on John's wife Elizabeth Proctor, who kicked Abigail out of the Proctors' home and ended Abigail and John's relationship. When witchcraft rumors begin, Abigail seizes the opportunity to begin to rid the community of those she does not like, including Elizabeth Proctor. 

John Proctor seems motivated by his torn feelings: he loves his wife, but he seems to still have some soft feelings for Abigail. In addition, John wants to think of himself as a good person, but he struggles because of his affair. John's sometimes contradictory actions and speech reflect his inner conflict and turmoil.

Deputy Governor Danforth seems motivated, at first, by a desire to rid the colony of witchcraft. Later, though, Danforth is much more concerned about maintaining his own authority rather than finding and upholding the truth, allowing the final executions to take place because delaying them would undermine his and the court's authority and lead to doubt about the guilt of those who have already died. Unwilling to do this, Danforth prefers to condemn those whom he likely knows are innocent.