If you stick with an 900/1800/1900 GSM (commonly called a Tri-band) phone, and you'll be happy pretty much everywhere except for Japan, South Korea, and parts of the Carribean.
More info on how cell phones work here:
http://electronics.howstuffworks.com/cell-phone.htm
Compatibility on GSM network coverage here:
http://www.gsmworld.com/index.shtml
[This message has been edited by skofarrell (edited 09-29-2003).]