Back in the 17th century, the area that would eventually become the United States of America was still just the "New World." Native Americans and European settlers lived side-by-side, but populations were small and there wasn't a whole lot going on besides bare survival. Modern historians like to picture white people stepping ashore with guns blazing, when in fact early relations between European settlers and Indians was often peaceful and cooperative.
The South American scene was considerably different. Most of the first European visitors weren't there for primarily religious reasons (as was true of the Pilgrims and Puritans in North America), and the natives they encountered were more violent than their northern counterparts. The result was a lot of bloodshed and fire, and names like Cortes and Columbus are still bad words in many South American countries.
In the New England colonies, however, God was uppermost in the minds of most people. Jamestown was the first English colony in the New World, and it wasn't particularly religious, but the second one was Plymouth and it was the first American home of the Pilgrims. The Pilgrims were Puritan in doctrine but Seperatist in practice, believing that the Church of England was beyond repair and that dedicated Christians had no choice but to leave it. They did, settling first in Holland, and in 1620 founding Plymouth Plantation in what would become Massachusetts.
The Puritans came not much later. Their intention was a little more ambitious than the Pilgrim project: not content with simply fleeing the shadow of a state church, they intended to build a Christian community in which the Law of God determined the civic laws, and where there was little distinction between sacred and secular law. Modern Americans often balk at this, but the Puritans weren't concerned with human wisdom, they were wholly informed by a desire to practice holiness and godly devotion.
Don't think they were all witch-hunters and dour black-clad killjoys, either. The Puritans enjoyed life as much as the next person, and while they were susceptible to ignorance and sin just like any other group of human beings, they were continually given to thanking God for the material and spiritual blessings He'd bestowed on them.
Their influence was largely responsible for the inclusion of Christian moral standards within the U.S. Constitution, for while the Enlightenment humanism of Franklin and Jefferson is clearly present, so too is the Puritan heritage of many of the Founding Fathers. As Christians, we also can thank God and praise Him for providing such forefathers for His children in the New World.