How can I make firefox behave like IE on a windows domain when requesting user credentials

Simple Answer. You can't. This is zoning facility because of IE's integration into the OS.

Correction apparantly this can be done as per this blog entry.

The setting is simple:

In the address bar in Firefox, type “about:config”
This will show all the settings for Firefox. 
In this list find this key “network.automatic-ntlm-auth.trusted-uris.” 
This is a comma-delimited list of all host names that you 
want to use NTLM with.
Just enter your host names like this: 
“host1.mydomain.com, host2.mydomain.com”

I know this is an old question, but it still comes up prominently in Search Engines, so I thought I'd add this.

A change just got released in FireFox 14. Set both of these to true in the FireFox about:config section:

• network.automatic-ntlm-auth.allow-non-fqdn
• network.negotiate-auth.allow-non-fqdn

You shouldn't need to add any URIs for this to work. Finally. If you're dealing with one or two hosts, it's fine, but when you have many machines... this is a saviour!

Open firefox and enter following address: about:config

Add sites/domains that are trusted into a following params. You can add multiple items by using , as a separator.

• network.automatic-ntlm-auth.trusted-uris
• network.negotiate-auth.delegation-uris
• network.negotiate-auth.trusted-uris