Many of the most intriguing places to see in Greece can only be accessed by road, and few are reliably serviced by public buses. One option is tour buses, but if you want to see Delphi when it's empty, as we did, that's a non-starter. Renting a car is not particularly expensive, and gives you amazing freedom of choice. It can also save money in other ways, for instance by allowing you to stay in small, out-of-the-way places that have cheaper rooms (as well as peace and quiet). All the familiar rental car agencies have offices in Greece, as well as some European and Greek companies. When deciding if a rental car is right for you, consider the following:
Driver's license - I just carried my U.S. license, which has worked fine in multiple countries, but some officials recommend getting an international drivers license, which is easy and requires no test.
Insurance - I used a credit card that includes insurance coverage when I rent a car, which saves a significant chunk of rental fees. Don't assume yours does - make sure.
Roads - Road quality varies widely in Greece. Around Athens and between major cities, there are Interstate-style highways. In Crete and outside metro areas most roads are narrow and often dug into the sides of steep hills or even cliffs. If you're intimidated by this type of thing, it may be more stress than it's worth. I kind of had fun with it, and if you're off-season there are few other cars on the road.
Traffic - Congestion around Athens is out of control. We made the mistake of arranging to return a rental car at the Athens airport following the last leg of our vacation. We also came close to missing our flight after the journey from Delphi to the airport took 2 extra hours of stop-and-go driving. We did not encounter traffic anywhere outside of the Athens area, so consider getting somewhere else before renting.
Manual transmission - It is very difficult to rent an automatic transmission anywhere in Europe, and virtually impossible in Crete. Make sure someone in your group is comfortable driving a stick, and comfortable doing all the driving if they are the only one.
Car size - Cars are smaller in Europe. You can rent a big car, but don't. The roads and parking spaces aren't built for them, and gas is way more expensive than here. Get something tiny and nimble, then wear those seat belts.
Road signs - On major roads, signs are posted in both the Greek and western alphabets. Everywhere else, it will pay to have a rough idea how to read the Greek alphabet. Note that just because something is also written using the Latin alphabet doesn't mean it is translated into English. Outside of major tourist areas, this is rare. Transliteration is a good job for the non-driver.