It has gotten harder than it used to be. If you really shop around you will be able to find some retailers that sell prepaid cards with limits up to $500. These are like gift cards, they're anonymous and you can't reload them.
With the reloadable cards, you buy the "starter card" but then you get a personalized card sent to you. The upside is that the presence of the card can still be a secret from friends/family. It's prepaid so it's not supposed to show up in credit reports, for instance. But, the reloadable cards require two things... The feds DO require you to provide an SSN in compliance with recent anti-laundering laws. And second, you do have to have an address you can send the card to, but it does not have to be your home address. Can easily be sent to work, a friend's house, etc.
The point of it being a "ripoff" that was made by a previous poster stems from the fee structure, the cards usually "burn off" a few dollars a month as a fee. The Walmart card, for instance, I believe charges something like $3 per month for each month you don't make a large deposit. I believe it's waived for a while if you load more than $1,000 on the card in a month. Also, Walmart charges $3 per load, unless you set up a direct deposit. I think there's a fee to make an ATM withdrawal as well. The Walmart card had a maximum balance of $3,000, I think that may be higher on some but I don't know. So you could be looking at maybe $50-$75 a year in fees to make a semi-private card work if you manage it carefully... Could be twice that if you use the ATM much. Definitely worth it if you need the discretion, definitely not worth it if you don't.