The home of the Patriots, Harvard, Gilmore Girls, Mark Wahlberg, and lobster rolls, New England culture and society is and always has been a major ingredient in the salad bowl of cultures that is the United States.
New England is usually defined by the region in the far northeastern part of the US comprising the states of Connecticut, Rhode Island, Massachusetts, Vermont, New Hampshire, and Maine (some consider up-state New York to be part of New England as well, but definitely not New York City itself). Boston is the region's main urban center.
Today, New England is a part of the cultural nation that Colin Woodard describes in his book, American Nations, as Yankeedom. Although Yankeedom today includes the Midwest and stretches as far as Iowa and the Canadian Maritimes, the characteristics Woodard attributes to Yankeedom are deeply rooted in New England history and society. From a few small-town settlements in Cape Cod and Massachusetts Bay, the first English settlers of this region have had a profound impact on the development of New England and American society.
For starters, it's important to understand exactly who these first settlers were. Many know the story of the Pilgrims. A group of a hundred or so English Calvinists sought freedom from the Church of England by creating a better life in the New World. They arrived in 1620 aboard the Mayflower and established the first New English colony at Plymouth, near modern-day Cape Cod.
Although the Pilgrims were in a sense escaping persecution, another group of English settlers arrived for similar, albeit slightly less tragic, reasons. The Puritans were a group of more radical English Protestants who, like the Pilgrims, were at odds with the Anglican Church and in conflict with the English government over religious policy. After unsuccessfully trying to settle down in the Netherlands, their aim was to create a religious utopia; a new Zion which would serve as the epitome of the perfect Christian nation. Governed by a strict Protestant doctrine, their nation would serve as a shining example in an increasingly deviant world.
The Puritans arrived in large numbers to New England throughout the 1630s and 1640s. They were not bound by noble overlords or distant joint-stock companies, so they were completely free to construct their nation as they pleased. The Puritans were in no way religiously tolerant, and their settlements were characterized by theocratic authoritarianism. On the other hand however, they were also very down to earth and politically free. They largely hailed from East Anglia, a greatly urbanized region in England dominated by an educated, religious, middle-class heavily influenced by liberal Dutch ideals.
This East Anglian culture was transplanted to New England through the "radical" Puritans.
The Puritans were in fact considered radical because they strongly opposed landed aristocracy, noble privilege, and conspicuous displays of wealth. Slavery was pretty much non-existent in early New England. Families comprised a large part of the demographic makeup of the English immigrants, and they all adopted the role of subsistence farmers (living only off of what they made). There were no plantations like those in the Chesapeake and thus there was no need for indentured servants or slaves. Furthermore, their hatred of feudalism and the traditional English hierarchical order led the Puritans to create an entirely new form of governance when establishing themselves in the New World.
Every community and town served as a self-governing republic. Most of the power was vested in a group of adult male townspeople elected by the town's men; the rest of the town would also gather for decision-making in town meetings, effectively forming two chambers of a mini-parliament.
The Puritans' middle-class background along with their strict adherence to the ultimate Christian ideal created the expectation of a literate populace. If they were going to blindly abide to God's word, they would have to be able to read God's word. Therefore, education was of utmost importance in New England society. Every town had a schoolhouse and every child was obligated to go to school, a stark contrast to almost all European societies at the time where education was largely a privilege reserved for the rich.
The Puritans were hell-bent on setting out to what they always came to the New World for: creating the ideal Protestant nation. They viewed the New England wilderness and all who lived in it (the Indians) as brutal savages. The Puritans believed that they were all hand-picked by God to do Him right and thus all violence against the environment and the indigenous peoples was justified. The Puritans did everything to recreate the English, civilized, landscape in New England. This included essentially exterminating the Indians, exemplified by wars against them like the Pequot War (1630s) and King Philip's War (1670s).
All of these major characteristics of Puritan cultural and societal identity both in New England and from their motherland in eastern England have gone on to greatly impact the development of Yankee culture as a whole.
A large chunk of the Puritan ideology was deeply rooted in Germanic and Anglo-Saxon notions of freedom. All were born with the same God-given mission to make the world a more perfect and less sinful place. Everyone was in it together; the failure of one could mean the failure of all. That, combined with influences of Dutch republicanism, created a strong attachment to community and democracy. In each town, government was a product of the people in that community, keeping an eye on each other and making decisions which aided the group's connection to God's word. As a result, democratic government became a major pillar of New England culture.
As the English began exerting tight control over the colonies beginning in the mid-1700s, New Englanders saw this as a return of the feudal, tyrannical control and the loss of their utopian society. Such attachment to republicanism and self-government is why Boston became the center of the American Revolution and home to some of the most radical and aggressive revolutionary leaders of the time.
Additionally, Puritan attachment to government would eventually turn into a core value of all New Englanders. The Federalist Party, one devoted to the rise of the central government in the new United States, had its home and strongest support in New England. The Puritan ideal of striving to achieve a more upstanding world is not only reflected in the American Revolution, but also in social matters, where New England has always swayed left. Today, some of the fiercest and strongest Democratic Party supporters exist in New England, a testament to their attachment to the ideal of greater government involvement as well. In small towns, town meetings are much more of a bigger deal than anywhere else in the United States, and community involvement is a big part of the New England identity.
Connections to the pursuit of greatness and Christian glory combined with strong republican ideals have helped to nurture what is today the American Creed or the concept of American Exceptionalism. Puritan and Protestant culture have created a quasi-religious political culture in the United States. The Puritans' mission to create a religious utopia also connects to the idea of Manifest Destiny which dominated American nationalism throughout the 1800s and 1900s and, to a certain extent, today.
Strong emphasis on education led to the creation of an educated elite in early New England. A lack of noble aristocracy meant that New England's establishment were comprised of intellectual families. The Adams family, which produced two presidents, are a perfect example of this. As a result, New England is now considered the intellectual center of the nation (only recently rivalled by the Left Coast and California). Harvard University is the oldest center for higher-education in the United States (founded by the Puritans themselves in 1645) and perhaps the most prestigious today. The strong connection to education has led to the development of some of the best universities in the world today, and Boston remains a city where the planet's brightest thinkers come together and study in two of the nation's foremost institutions, MIT and Harvard. Those two schools join a list of a number of other prestigious universities in the region including Yale, Brown, Dartmouth (also founded by the Puritans), and Cornell.
All in all, the Puritans' impact on New England and American society is immeasurable. To be clear, the Puritans are not the best people to look up to: they were incredibly intolerant and brutal, but America wouldn't be what it is today without them.
Sources:
"Chapter 4: Founding Yankeedom" in Colin Woodard's American Nations
"The Puritan Legacy" in Adam IP Smith's essay American Political Culture