Bobby Habib - My findings on SharePoint / MOSS, Web Part Developments, etc. Information I think will help the SharePoint Community. All posts are provided "AS IS" with no warranties, and confers no rights.
Whats the bloody Point!
How do we get the OWA Web Part to work without prompting you to add user credentials and to autodetect the user without prompting for a password?
Hmmm...Interesting. 
The best workaround I have seen for this so far is to set up x2 web sites on your OWA server. One web site can be configured with FBA [Forms Basic Authentication] or Basic Authentication [mail.yourcompany.com] which is used for primary OWA use within your organization and the other web site [spmail.yourcompany.com] is configured with Windows Authentication which is used for just SharePoint web part usage.
Using the windows authentication site [spmail.yourcompany.com] within your web part will automatically log the user onto the OWA server without re-prompting for the password.
Makes sense when you think about it. 
About bobbyhabib
I am Currently working as a Freelance Sharepoint Technical Consultant / Developer.
I have done Technical Consulting / Development for such companies as BT, Computer Science Coprporation, Sony BPE, GlaxoSmithKline, Media Maker, Business Links, Plumtree Professional Services, Centrica, Hewlett Packard Professional Services, Napp Pharamceuticals, 3i Group plc, Chapter 26 and currently working for Microsoft.
Product and Services have included work with C#, .Net, ASP, ADO.Net, XML, SharePoint 2003 to MOSS, SharePoint Migrations, SharePoint UI Customisation, Plumtree.
I have been developing in .NET technologies since .NET was first in beta and have been designing and developing software solution for leading companies since 1995.
Areas of Interest:
MOSS, Collabrative Technologies, AJAX, Web Services, Workflows, MOSS Search, UI SharePoint Customisation, Development Patterns, Web Parts, SharePoint Migrations.
During my spare time when I am not being a geek, I love to spend time with my beautiful wife and my two adoreable kids. Love walking, travelling, gardening, reading, pool, rowing, badiminton and running.