The idea of democracy that we possess within our government today is based off of the system of democracy that the ancient Greeks from Athens had established. In edition to democracy, our ethical codes and ideas of individual thought and expression are greatly influenced by the philosophers Plato and Aristotle. The education and techniques for education we have within America is influenced by the Socratic method. Entertainment and theatre within America is influenced by Greek tragedies and is also influenced by the theatre of the ancient Greeks.
One interesting fact is that architecture of government building and many other buildings within America is greatly influenced by Ancient Greek architecture.
Hope this helps. I wasn't sure how many things you needed to know.