<p>I need to connect to Outlook through ASP.NET web application using user credentials. What are my options? </p>

<p>FYI: User logs into the web site by using Windows Authentication. I'm working with Outlook 2003. </p>

I'm going to do something similar, and I don't see a reason it wouldn't work: write an
Outlook Addin
that uses
object remoting
to communicate with whatever other services or tools you're working on.  Since it's an ASP.NET application, maybe you want to use a web service instead of object remoting.
Do you want the ASP.NET application to start Outlook if it's not already running?
Is one Outlook process going to be shared by many users, or do you want to connect to user-specific Outlook processes?  Do you want the ASP.NET application to act as a server that Outlook tries to connect to, or the other way around?
If the edge cases are complicated, you could try writing a Windows Service to act as an intermediary or gateway between the two e.g. a service that runs on each Outlook machine and starts Outlook on demand.