A lot of my clients are using “google apps” as their mail service, and outlook as their mail client.
I just got a call from one of them saying outlook 2007 was giving “Enter Network Password” prompt no matter what he did.

we tried everything, reinstalled the Outlook account, changed the password, disable/enabled POP and IMAP, but no… the solution is doing some google voodoo on this page: https://www.google.com/a/[your domain].com/UnlockCaptcha. (change [your domain] to… the domain you’re using for google apps)

you can read the entire help section at:  http://mail.google.com/support/bin/answer.py?answer=14257

good luck, and don’t forget to uninstall Outlook after this.