Suppose there was a blockchain that allowed an 'OpenTransactions Server' to 'checkout' some currency to use on their server.
Now suppose that every time the server signed a receipt it also published a transaction to the network to update the hash of the last signed receipt in the blockchain.
The blockchain could then honor requests to withdraw money even if the server went away by simply presenting the receipt.
Then all that would be required is a means to AUDIT each OT server to make sure that it never issues more receipts than are valid, which I believe there is already such a system in place (or at least designed).
Now connect all of these OT servers together through BitMessage.
The end result is that you could have entirely secure anonymous transaction with complete destruction of your transaction history. The existence of the OT servers could even be hidden from the user.
Now combine this with something like BitShares and we will have pulled it all together in an amazing way!
Awesome! Check out the auditing page of the OT wiki while you're collecting your thoughts on this:
https://github.com/FellowTraveler/Open-Transactions/wiki/Auditing