Great question. There are dozens to choose from, so I'm going to narrow it down to one example of each.
Events - The writing of the Mayflower Compact, the first colonial document dealing with self-government, town meetings, and the concept of majority rule. We would borrow from this idea, among many others, later in our history when democracy was developing.
Ideas - Separation of Church and State was first discussed in the New World in Roger Williams' Bloudy Tenent of Persecution. While it was mostly dismissed by the Puritans of the time as heresy, it has become a key feature of religious tolerance in the US, which became widely accepted by the Framers at the time of the Constitutional Convention.
Social Patterns - New settlers from Europe, especially those that came to the Middle and New England Colonies, did so for land ownership. The growth of the colonies into a population with so many landowners - yeoman farmers as they were called - led to a large and diverse voting population which has always promoted democratic sentiment. Unlike Europe where the land was owned by Lords and royalty, Jefferson imagined an agrarian republic, where each landowning male had a say:
"Cultivators of the earth are the most valuable citizens. They are the most vigorous, the most independent, the most virtuous, & they are tied to their country & wedded to it's [sic] liberty & interests by the most lasting bonds."