If you want to use OWA webparts with Integrated Authentication or Basic and have it default to the user that is logged on, the steps are simple - leave the username blank (see below).

But if you have done that you may be surprised to find that it continually prompts you to log in on that page EVEN THOUGH YOU ARE ALREADY logged on.

Not putting in the info gives you a beautiful 401 error:

Luckily the resolution is simple.
What you want is that you will be logged on to the mail server with the current user name and password. But if you open up the security settings on your browser you will find out that this is not the option.

There are two ways to resolve this - both involve changing the setting. You can either change the zone that it defaults to (ie make Local Intranet always do 'Automatic logon with current user name and password') or you can put the mail server in the Trusted Zones.
I like the latter.
Go into the Securities tab, click on 'Trusted Sites' icon and then click on the 'Sites' button.

Once you are in there you can add the FQDN of the mail server (since you will be using its cert)...

Voila!!!
Note: if you want to do this on a larger scale I would suggest you turn to your handy-dandy Group Policy editor. You can find what you are looking for User Configuration / Windows Settings. I will leave the rest of the steps up to you...
