Sprint and Verizon have "worldphones", but they are hybrid CDMA/GSM phones. I would check where you are going to travel for the GSM frequencies they use. If you want to be sure, then get a quad band phone, with 850/900/1800/1900 MHz. The US uses 850 and 1900, while much of the world uses 900/1800. Some countries are installing 850 MHz networks, though.

Korea and China and, I believe, Japan, have other networks, more advanced than what we use in the US.

If you want an "unlocked" phone, then you are looking for GSM. That will allow you to use local SIM cards instead of roaming internationally. You will have to check the prices for that to see if it is cost effective to buy local SIMs or just roam.

From what I understand, it is far easier and cheaper to unlock Nokia phones than Motorola ones, but Motorola makes the most quad band phones. I do believe that Nokia has a quad band coming out in the near future. I have a Motorola V505 which I chose because of its Bluetooth and quad band capability.