Error Trapping The Dreaded Refresh

My problem basically is as follows:

1) User enters their details to create a new account in my db.

2) They press the submit, the system successfully creates their new account
and then displays a page saying 'well done you've created your new account'.

3) The doofus (or clever clogs) clicks the Refresh button, which in turn
submits the details back to the db and creates a duplicate entry in my db.
I don't have a duplicate account num, as the system takes the max last one
and adds one to it so really no errors are generated, but it does mean that
they have 2 accounts now.

As mentioned above, this scenario crops up when doing a New Account page and
when they've just posted their order via the shopping cart final page (shall
we say). The latter worries me because duplicate orders would cause a lot
more hassle.