There are two important things to consider regarding using electric devises in Greece & Cyprus.
The first is voltage. The United States uses 110 volts while Greece & Cyprus use between 220 and 240 volts. If you plug an American appliance into the 220 volts without checking if the power supply is designed for the increased voltage, you will destroy the appliance. However, many American electronics are sold with "dual" power adapters. For example, the power supplies for my mobile phone, digital camera, laptop, and I-pod are all designed for 110-220 volts. On the other hand, my electric razor, hair dryer, and wireless router are not. To find out if your power supply is designed for 220, simply read the small print on the power cord. (see this website for more detailed information: http://goeurope.about.com/cs/electricity/l/bl_electricity.htm)
What is a converter and do I recommend you get one? A converter will convert the volts from 220 to 110. But, I do not recommend you bring one. They are very heavy and not inexpensive. If you need it for your hairdryer or razor, I recommend buying a travel dryer or razor.
The second important thing is plug type. Greece and Cyprus use two different types of plugs. So, you'll need two types of adapters, which will only allow you to plug your American appliance into a European socket; it does not adjust voltage. In the U.S., you can pick it up at a travel store or Target. The Learning Abroad Office also sells them. In Europe, you can pick one up at a supermarket, kiosk or at the airport.
Greece uses this type: http://users.telenet.be/worldstandards/electricity.htm#plugs_f
Cyprus uses this type: http://users.telenet.be/worldstandards/electricity.htm#plugs_g