Whether you're American or Canadian, your passport and driver's license are all you need in most European countries. However, some countries also require an International Driving Permit (IDP).
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When visiting another country as a U.S. citizen:
Your state driver's license is valid while driving in Canada and Mexico.
In other countries, you may need to get an International Driving Permit (IDP) for foreign drivers.
If you're a non-EU citizen that would like to rent a car in Italy, it's essential to hold an International Driver's Permit. The Italian car rental might not ask for it, but it is required by law that you have one, and it may be requested during a police check.
While renting a car isn't necessary or even advised if you're only visiting major tourists city (you can't even bring your rental car into the old town Florence, and having a car in Rome is a very bad idea not just because of traffic but also because many main attractions are only accessible by foot anyway), if you ...
Tourists are allowed to drive in the Netherlands on a valid state license, preferably in combination with an International Driver's License which may be obtained in the United States through the AAA.
U.S. citizen tourists/temporary residents with stays less than six months with a valid United States driver's license can drive in Greece with their U.S. license. For stays more than 185 days in Greece: A Greek license may be required.