Internet Explorer
This can be accomplished by going into Internet Options, selecting the security tab, then selecting "Local Intranet," sites (and selecting advanced), then adding the site you wish to save as a local intranet site.




Chrome
Chrome may save passwords automatically after you enter them the first time and select to "Save password" after seeing the prompt.

Firefox
Similar to Chrome, Firefox will ask if you want to save passwords automatically after you enter them the first time you access a password accessible intranet site and can be verified or updated by going to the Security settings.

