I have the beginning of something like this.  It's mostly like what Gavin described.

Some more rpc interface:

move <fromaccount> <toaccount> <amount>
   Move from one internal account to another.  I think blank account name ("") will be your default account.  If you sell something to a user, you could do move "theiraccount" "" 123.45.
   Is "move" the best name for this?  I shied away from "transfer" because that sounds too close to sending a transaction.

I'm thinking a new function getaccountaddress instead of overloading getnewaddress:

getaccountaddress <account>
   Gives you an address allocated from getnewaddress <account>.  It'll keep giving the same address until something is received on the address, then it allocates a new address.  (It automatically does what the sample code I posted some time ago did)

Would these commands make it possible in simple cases to implement your website without needing a database of your own?