Recent law changes have made it more difficult for a US citizen to rent vehicles in Greece.  Many places are now requiring you have an IDP (International Drivers Permit).  While some smaller rental places may not require this license, we highly recommend getting one prior to your journey if you're planning to rent a vehicle, ATV or scooter in Greece.  Luckily it is easy and inexpensive to attain an International Drivers Permit.  The best method we've found is through AAA. Here is what they state you'll need:
Download and fill out an application, and bring it to your nearest AAA branch office*.
Two original passport pictures (also available at AAA branch offices*).
A valid U.S. driver's license.
Pay $20 USD permit fee and you're ready to go!
*You can also get the permit through the mail if you can't visit an AAA office.  You can find information here.