My ideal online payment solution (and I think it'll happen later) is for everyone to have a number they put into a site to buy. Then they have to log into online banking and approve the charge. There'd be a description of the company and the charge automatically with the debit, and "Approve / Decline / I Don't Know This User" choices or some such.
It'd reduce fraud to near-zero levels, and I don't think it'd cost too much to set up. Credit cards will live on for a long time as short term credit, but I reckon banks could offer that at much more reasonable rates with a much better idea of people's finances and credit profiles. And with widespread enough adoption, merchants could start telling CC companies to take a hike. Heck, the bank could even make it a "card that you control" or something to not break from the card tradition.