Credit: William Hilsum, Superuser
https://superuser.com/questions/106917/remote-desktop-without-a-password

By default, Windows will not allow the logon over a network with a blank password. There is a KB article that details how to allow blank passwords for network logons.

You can disable blank password restrictions by using a policy. To locate and change this policy:

Click Start, point to Run, type gpedit.msc, and then click OK to start the Group Policy Editor.
Open Computer Configuration\Windows Settings\Security Settings\Local Policies\Security Options\Accounts: Limit local account use of blank passwords to console logon only.
Double-click Limit local account use of blank passwords to consol logon only.
Click Disabled, and then click OK.
Quit Group Policy Editor.
NOTE: By default, this policy is on (enabled).