It is important to note that, although there are GSM networks throughout the world, they are are generally incompatible with one another due to the fact that the North American GSM network operates on the 1900mhz range, while the European, Asian and South American Networks operate on either 900mhz or 1800mhz. There are bi- and tri-mode phones that will work in both networks, but they must be specially designed for the purpose.
However, because GSM handsets employ "SIM" smartcards, you can rent a phone in the contry your a visiting, insert your SIM card and it becomes your phone, and your home account will be billed.