I believe most (if not all) prepaid Visa, MC, and AMEXs allow you to register a billing address which enables you to make online purchases. The exact process for doing so depends on who issues the prepaid card. Prepaid AMEXs purchased directly from their website require you to call into their customer service line and they will allow you to register a billing address. Prepaid Visa cards from giftcard mall allow you to register a billing address through their website.

These are just two examples, but just take a look packing that came with the prepaid card, or call the phone number on the back of the card itself for more info.