The best thing is to buy a quad-band GSM phone over here, get it
unlocked, and bring it to Europe with you.

You can order a prepaid SIM card that works in multiple countries. I use
MaxRoam ("http://maxroam.com/"). Also check GeoSim
("http://www.globalsimcard.co.uk/") but their back end provider went
down for a few months, and now they're back. Their attraction is free
incoming calls.

There are many other prepaid, multi-country SIM cards available. Each
has different rates and features. MaxRoam gives you a U.S. number (and
you can get more numbers in other countries). Most of the prepaid
multi-country cards don't give you a U.S. number. A U.S. number can be
useful if you want to forward your Verizon phone to your international
phone, though there are inexpensive ways to forward your Verizon phone
to a foreign number as well, by using a service like My Global Talk
("http://myglobaltalk.com").

T-Mobile Prepaid sells the Motorola V195 quad band phone (with Bluetooth
but no camera) for $40, including an extra $25 airtime card. However
you'll have to get an unlocking service to unlock it for you. This is
what I did. Supposedly they'll unlock it for free after 90 days, but I
couldn't wait that long.
"http://www.t-mobile.com/shop/phones/prepaid.aspx"

Yes, I had a direct experience with renting a Vodaphone through Verizon for
a trip through Europe. It was one of the disgracegul experiences of my life.
One day, in the middle of the trip, I found the phone shut off, without any
notification.  My son had just had emergency surgery that day and I actually
really needed the phone. I was on a cruise, so I had no easy way of
exploring the problem until I got home.

When I returned, I found out that my charge card company had noticed charges
being made in Europe, at the same time as Vodaphone was updating their
charges in the U.S. for phone usage, so the charge card people shut down the
card, and Vodaphone, unable to update their fees, shut off my phone!

Now I am not an unreasonable person, but the phone, whose purpose was to be
used just in the event of such an emergency, was not accessible when I
needed it most.  I believe that Vodaphone, being the ones with the
experience in that business, had an obligation to inform me, the
inexperienced consumer, to notify my charge card company that charges would
be appearing from two different locations (something I couldn't have known),
or to advise me not to use the same card for the phone that I would be using
on the trip, something which I never could have conceived of on my own
except through some devine intuition.

Needless to say, I was pretty pissed off. Vodaphone, for their part, could
care less, did not offer an apology, and insisted that I pay the bill.  I
did, but I'll never use them again. The experience was too bizarre. I
recommend finding another way. Buy an 8830 and save yourself a lot of
unneeded aggravation.