According to Arthur Miller's The Crucible, what circumstances motivate people to lie?

Love, or lust, seems to be what motivates Abigail Williams to lie.  Early in Act I, she tells John Proctor, her former lover,  that there is no witchcraft involved in the illnesses of Betty Parris and Ruth Putnam.  However, her later accusation of John's wife Elizabeth seems to have been done to get Elizabeth out of the way so Abigail and John can be together again. 

Greed also seems to motivate characters to lie.  A...

Love, or lust, seems to be what motivates Abigail Williams to lie.  Early in Act I, she tells John Proctor, her former lover,  that there is no witchcraft involved in the illnesses of Betty Parris and Ruth Putnam.  However, her later accusation of John's wife Elizabeth seems to have been done to get Elizabeth out of the way so Abigail and John can be together again. 

Greed also seems to motivate characters to lie.  A friend of Giles Corey heard Thomas Putnam imply that he encouraged his daughter Ruth to accuse one man of witchcraft so his land would go up for auction, making it available for Putnam to purchase.  According to Corey, only Putnam has enough money to be able to afford such a big piece of land.

It is possible the other girls were compelled to lie out of fear of Abigail, especially after she promised to come to any who spoke against her "with a pointy reckoning" in the middle of the night.  Mary Warren, certainly, seems to lie, accusing Proctor of witchcraft when it becomes obvious that Abigail is going to cry out on her next.

Tituba lies out of fear as well, but not out of fear of Abigail.  Tituba lies out of fear for her own safety.  After Reverend Parris threatens to beat her and Putnam says that she must be hanged, Tituba (falsely) confesses her involvement with the devil so they will, she hopes, not punish her.

Some characters -- like Deputy Governor Danforth -- lie or cover up the truth as a result of their desire to retain authority.  It is fairly obvious, especially by Act IV, that Danforth's primary concern is maintaining the authority of the court and his decisions, rather than making sure that the truth is revealed by the court.  Thus, even when it seems as though Abigail and Mercy Lewis have been lying, he ignores their possible guilt because it would contradict the righteousness of the court's actions so far.