The notion of American exceptionalism is rooted deep within our national consciousness. It probably started with the Puritans, who our history (read: propaganda) records as having come to the New World in search of religious freedom. The truth, as is often the case, is a little more ambiguous. Yes, the Puritans were seeking religious freedom, but it was the freedom to be rigid, repressive asshats. Look at it this way: 17th century England was a pretty authoritarian place by our standards, and the Puritans were too uptight even for them. And like many religious zealots, they believed God was on their side and that they were the "chosen people."
This idea directly translated into the concept of manifest destiny — that it was the white man's destiny, in other words, to conquer the entire continent, from sea to shining sea. But it also found form in the more generalized form of American exceptionalism, the idea that our country is somehow special and different from other countries. As I said, all countries feel that way. It's human nature. But Americans take it to extremes. And for the past hundred years or so we've had the political, economic, and military clout to back it up. Winning two world wars sure didn't do anything for our humility!