Start with a bank-to-bank funds transfer system built on itemised invoices. You can create an itemised invoice with your bank, and they keep it on file, and generate a unique identifier for it. You pass that identifier and your bank's BSB code to your customer. They go to their bank and enter the number, which displays the invoice, fetched from your bank by the number. When they approve it, the appropriate total, as defined in the invoice, is transferred to your bank account. That's the backbone of this system.
Now for the cool part. Say you're at a market, where a lot of small businesses have booths to sell their wares. Using this invoice system and smartphones, these small market businesses can accept electronic payments rather than handling cash. The stall owner can pass the invoice numbers to customers via QR codes, so that there are no mistakes. The whole transaction from end to end would look a lot like tallying up an order on a calculator app, showing a generated code to the customer, then confirming receipt of the funds via the same app.
As long as the banks are all on board, and the apps are available for all major smartphone operating systems (or as mobile-friendly websites), there's no reason for any of this to be tied to a particular institution or device, and no personal information needs to be exchanged between customer and seller, so privacy is maintained (as long as invoice numbers are random) and security is aided by the disposable nature of the invoices.
Mokalus of Borg
PS - Hopefully such a system would be provided for free.
PPS - Then again, banks do love their fees.