We see Greek mythology in: movies and books. (Hercules, Clash of the Titans, and Wrath of the Titans.
Greek architecture is known for it's columns. There are three types of columns: Doric, Ionic, and Corinthian. Other types of Greek art include pottery, sculptures, and paintings. Every city had a temple that was dedicated to a specific god. They went there to worship and make sacrifices. Some leaders like Pericles and Alexander The Great, spread Greek architecture through out Europe.
We see Greek influence in architecture today in important buildings. The White House Capitol Building, The Supreme Court and The Lincoln Memorial all have columns that show Greek influence.
We still see doctors use the Hippocratic oath and we use pi.
Things in their democracy we see now in our democracy are: Every one can voice their opinion, We have to be 18 to vote, and we have term limits today. (4 years for president)
Today we have some of the exact same events today like: Javelin, boxing, shot-put, long-jump, and running. And we still have the Olympics.