No, just like a PSP3, you don't have to pay any monthly fee at all. But unlike the iPhone, you need WiFi wireless internet to get it. The only cost via internet is optional. That is iTunes, and the Apple store, witch have addon applications for the iTouch, witch some cost money (payment via card), and some are free.
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No you do not pay a monthly bill for the ipod touch if you have internet on it i think anyway you might want to check agian. :)