The term Puritan came as a term of abuse for Anabaptists; this term is slightly more accurate for those who came to America as they had the strictest views on sexual morality, disapproval of recreation, and the proclivity of imposing their views upon others. Symbolically, Nathaniel Hawthorne in his novel "The Scarlet Letter" portrays this rigidity with the first chapter opening in view of the iron-doored prison. The Puritans of the Massachusetts commonwealth were extremely radical and punitive; their social experiment took the form of the Anabaptist theory as they attempted to create a theocracy of their commonwealth's government.
Because their creed stated that one must have a strict accounting for sins, and because women were all perceived as corrupt since they descended from Eve, punishments for women's sins were often more severe than for men's, especially in the seventeenth century. In these early days of colonization, the penalty for adultery was death, although there is no evidence of this extreme measure having been used. In most cases, those women who had committed adultery were usually fined, publicly whipped, or flogged, or branded.
It is this excessive and unforgiving nature of the Puritan that Hawthorne wishes to portray in his narrative of Hester Prynne. Also, since Hawthorne states in his novel that Hester "was not a Puritan," the rulers of the strict Anabaptist community may have imposed the ignominous punishment upon Hester to further humiliate her. This attitude of cruelty and sanctimony can certainly be supported by the conversation among the women who wait outside the prison to see the beauty of whom they are jealous scorned and made a pariah:
'Goodwives,' said a hard-featured dame of fifty, 'I'll tell ye a piece of my mind. It would be greatly for the public behoof, if we women, being of mature age and church-members in good repute, should have the handling of such malefactresses as this Hester Prynne. What think he, gossips? If the hussy stood up for judgment before us five, that are now here in a knot together, would she come off with such a sentence as the worshipful magistrates have awarded? Marry, I trow not!'
The Puritans' attitude towards adultery has become most connected with the punishment of Hester Prynne in "The Scarlet Letter." However, her punishment was not really what was usually done (although there were cases in which women were required to wear an "A").
It was possible, in some cases, for people to be executed for adultery in Puritan times. One example of this, as seen in one of the links, is Mary Latham in Massachusetts in 1641.
Although Mary Latham was executed, the much more usual punishment for adultery was a public whipping.