Cannot map printers without admin rights on Windows XP or 7

This will generally occur if you need to install a printer driver that is not approved by Microsoft.
You will find it either fails or asks for the administrator username and password.

There are various Group Policy Adjustments that need to be made.
On Windows XP, follow this article ->

On Windows 7, you need to disable this GPO (same policy as that for XP in the article above, but different location):
Computer Configuration/Policies/Admin Templates/Printers/Point and Print Restrictions

Make sure you apply Computer Configuration Policies to OU’s with Computers, and User Configuration Policies to OU’s with Users in it (or lump them both into one policy and appy them to both Computer and User OU’s). Then everything should work find once the policy refreshes on the PC.