One approach is to use the SOAP API to automatically establish a session using securely stored credentials. Once the session is established you can use the Session ID and Server URL to send a web request to the page that contains the Data Export, parse out the download links, and then pull the zip files down and store them locally. Depending on the duration of the transfer you may need to recover from a lost session.
The usual caveat applies to this approach as some of the steps aren't using the provided APIs. Salesforce may at their whim break the ability to extract the zip paths.
Based on the above solution we have made a free tool using .NET here at work that can automatically download the Data Export from the command line and/or the included GUI app.
This can be useful when the number of zips to retrieve grows large or you want to automate the download process.
See FuseIT SFDC Data Export.
You might also like to vote for the idea:
Weekly Data Export - Ability to automate file transfer via web service