If you want to have a phone that works in Europe then you are going to need
one that uses the GSM standard. You will need a tri-band, or quad-band GSM
phone if you want it to work in both the USA and Europe. Tri and Quad refers
to the number of frequency bands the phone will work on. As the USA and
Europe use different frequency bands, a phone intended solely for the US
market will not work in Europe. You can get a quad band phone for "free"
with a 2 year contract these days, so the cost barrier is no longer an
issue. If you want additional features on your phone (camera, MP3 player,
coffee maker, etc.) you will have to do some additional research. The two 2
big carriers that use the GSM standard are Cingular and T-Mobile. Both offer
a selection of plans including nationwide coverage. Of the two I think
Cingular offers better coverage in the USA, but that is my opinion (lest I
get a verbal tar and feathering from someone). Both offer international
roaming, but you will need to ask for this feature to be switched on and you
need to be in good standing with either carrier (pay your bill on time,
etc.). I have heard figures of 90 days mentioned as a waiting period after
signing a new contract. You do not say where you will be visiting, but both
Cingular and T-Mobile (a German company) have roaming agreements across
Europe. Be warned that roaming charges are significant and a more cost
effective option is to buy a pre-paid SIM in the country you are visiting.
If you decide to go the pre-paid SIM route then you will need to get your
phone unlocked so that it will work with another carriers network. I have
never done it (my V400 was unlocked), but I believe Cingular will unlock
your phone for you, but it takes time, so plan ahead.

I have probably missed something, but there are plenty of helpful people who
will fill in any gaps.