The Puritans didn't last long in America, and the previous post outlines many of the reasons why. It was a difficult balance to walk between heaven and hell, and it didn't take long for people to finally quite trying to walk that tightrope. The Puritans lived in a world without forgiveness; they believed in penitence and penance, for sure, but forgiveness was in short supply. Eventually people got tired of always feeling as if they were under condemnation. This view of sin permeated the entire culture, causing paranoia and finger-pointing in an effort to avert the personal accusations and condemnation of sin. Ultimately, the movement died a natural death.
I would say that one of the most dominant Puritanical beliefs that still lingers, to a large extent, was its categorization of God. Simply put, the Puritans had a very demonizing view of the divine and the role of humans within such a scheme. The Puritans believed strongly in original sin, and to this extent, ended up ensuring that humans never deviated from the belief that they were naturally sinful. Such a belief ended up affecting New England, and all of America to a degree, with a challenging view of God. On one hand, individuals sought to believe in redemption because of the democratic experience that they had inherited, a political system that stressed the idea of "forming a more perfect union" and trying to "get it right." Yet, this was opposite of the Puritan point of view regarding spirituality where God was proverbially unhappy with individuals regardless of acts. Both were set on a collision course by the Puritans, revealing a division in how individuals viewed themselves and the world. What the Puritans did in Massachusetts was embodied by all of the New England Colonies, resulting in a very paradoxical view of religion and a conflict, to a certain extent, in the New England Colonies.