I think that the Mayflower Compact is a great example of an event or idea that helped to shape American Democracy. As mentioned above the Compact dealt with self government and many of the same ideas were used in our Declaration of Independence and Constitution.
The Iroquois Constitution is thought to be a precursor to our eventual Constitution. In the earlier document can be found, among other things, the foundations of a representative government (in which, interestingly enough, men served as representatives but were elected by the women). These representatives gathered from many tribes to conduct business and make decisions which would ultimately benefit the entire native nation--quite similar, of course, to the representatives from each colony who would one day gather to write the U.S. Constitution.
Just to add an additional event that helped shape American democracy. The Great Awakening was a religious event in the colonies in the 1730's. Though it was religious in nature, it had political aspects, too. These Great Awakening ministers preached that everyone was equal in the eyes of God--that is, all had the same chance of being saved and reaching heaven. This idea of religious equality spilled over into politics. People began to see that they were politically equal as well. That the king was no better than themselves. In this way, the Great Awakening helped spark rebellion against the king. And of course equality is one of the founding principles of this country.
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."