Unless you're only going to be there for a couple of days, you'll be much better off if you buy a phone and get prepaid SIMs once you get there. It costs as much to rent a phone for a week or two as to buy one.
You can get a euro 900/1800 or triband 900/1800/1900 phone on ebay for under $50. Be sure to get one that has been unlocked to work on any GSM carrier. (Not "can be" unlocked, any phone can be unlocked, in theory.) When you get to Greece and to Turkey, buy local prepaid SIMs, or if you want, you can buy them online ahead of time which costs more but you know in advance what your numbers will be.
If your goal is primarily so that people in the US can reach you, and you have a Cingular, AT&T, or T-Mobile GSM phone here, you can use your current SIM in a euro phone. The per-minute rates are quite high, but you keep your own US phone number. Call them before you go to get international roaming enabled, and ask if they have an addon plan with lower roaming rates.
Another possibility is a "universal" SIM with a Liechtenstein or Monaco phone number. Their rates are not as cheap as a local SIM, but you can get one SIM and use it all over Europe and Turkey at the same not too awful rate.