Greece is a Member-State of the European Union and has signed the Schengen Agreement.While traveling within the E.U., you only need your Identity card. However, a passport is necessary for a number of other transactions, such as currency exchange, purchases, etc.
If traveling from another place you can take a look at the link below showing, from the Hellenic Ministry of Foreign Affairs, the list of countries and whether or not you need a visa to enter Greece.
Moreover, US citizens can visit the International travel guide for more details.
If you wish to contact your local embassy or consulate, please check the link below