There are many areas in which we can find puritan influence today. At the top of the list stands the structure of the family as we know it. The essence of social order lay in the authority of parents over children and in those days, husband over wife. Marriage, as we know it today, played an important role in creating the fabric of their society and till this day we see it's effect on us.

Another point in which they were influential is the fact that today the American society condemns Alcohol abuse and inappropriate sexual  behavior. The puritans themselves allowed the drinking of alcohol in moderation and the partaking in sexual intercourse within one's marriage but they where against abusing these privileges. This is something that we can find in the American society till this day.

Some researches think that the puritans put down the foundations needed for the American democracy to form. This is a point still under dispute but it seems that there is strong evidence pointing in this directions.

Hope I was able to shed some light on the subject.