There are pre-pay debit cards from AmEx, VISA, and MasterCard in most supermarkets, pharmacies, and other places. You put money on those. The downside are the monthly, per-transaction, and reload fees.

EDIT to add: There are also Gift Cards for iTunes, Google Play, Barnes & Noble, Sony, and many others that sell online. That's another way to pay. The downside is having a balance too small to spend on anything without getting another card.