The rest of the world is on a different band that the GSM we use in NA, so your NA GSM phone will not work unless it has the GSME bands in it.
I had TMo and one day it stopped working at my house. I called and they said the tower had a problem, but they didn't want to repair it.
I switched to Verizon, I live way out in the sticks and need the cdma coverage. But, when I am in London (England), Dublin (Ireland), Hong Kong, or whatever other place I am in, I need the phone to work. The world BlackBerry covers all of that, and I keep my same number. Plus my UK GSM card works in it too so I can have my $.05/min rate to the US via Orange. I got it covered.