Simple answer is "almost never." They are basically gift cards, nothing more. It's understandable that some people have trouble obtaining a bank account, but, when/if you can, you should avoid using pre-paid credit cards.
As stated above, pre-paid credit cards are basically gift cards. In fact, many of us have received these cards AS gifts in our stockings or event cards. Getting these are fantastic gifts and we all love them, however, there is virtually no upside for consumers to get pre-paid credit cards for personal use, especially when considering the normally high fees that are associated with these cards. To top it all, pre-paid cards do not report to your credit report. If you're going to use your own money to obtain your own pre-paid credit card (that you will also use), you may as well put your spending habits to work building your credit!
An alternative to pre-paid credit cards are SECURED credit cards. MOST secured credit cards report to all 3 credit bureaus; you'll be adding history to your credit report every time you use these cards. Important NOTE: Your deposit is the collateral for which you are granted the line of credit. It is NOT meant to be the replacement to making your payments on your secured credit card. Make your payments like you would any other bill.
For a list of secured credit cards with some great rates, CLICK HERE!