Most CDMA phones (Verizon and Sprint) will only work in the US. To work in overseas areas, you really need a GSM phone (Cingular or T-Mobile) but I have heard that both Sprint and Verizon offer some type of international phones if you set it up in advance of the trip abroad. You should talk to your carrier.
Judging from the many posts concerning overseas travel, T-Mo is the best for Europe. Not sure about Japan and the Far East as they seem to be using a different standard, however, I have seen some posts where the 87xx on both Cingular and T-Mo have worked in Japan.