If you are traveling in Europe and you don't already have a GSM phone with service, don't rent a phone. Instead buy a cheap "unlocked" cell phone. These are phones that are not "locked" to a specific carrier such as AT&T, Sprint, Worldcom, etc.
I've seen them as low at $75. You then just purchase a "sim" card for the country you are in and you have service.
The upside is that you own the phone if you travel again you don't need to rent a phone, the price for calls using the sim cards are much cheaper than the rates for a rental phone, you can recharge the sim card on your next trip, and you don't have to buy a new one.
The downside is that you won't have a US number for people to call, your number can change from country to country, and you have to purchase a sim card for each country.
Overall it is much cheaper to purchase the phone and sim cards, but it is a bit more of a hassle.
You should also check with your current cellular provider and see if they offer gsm service.