How can I download the backups ClockworkMod creates to my PC?
The ROM Manager app has an option in the Manage and Restore Backups to Download Backups. You might want to try using it to create backups and download those backups to your computer.

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Choose Download Backups and you will see:



Provided your phone and your computer are logged into the same network you can point your browser to the address shown on the screen and choose which of the backups you would like to transfer to your computer.

It will take a while depending on the size of the backup.

This may be a feature of the Pro Version but the Pro version is worth every penny.

Good Luck.