I have installed Visual Studio 2008 and am running it as a non-Administrator user.
I have a Web Application project I am developing and would like to debug it using
I've never tried this, but it might be worth a shot.
While logged in as an administrator, you could change the identity under which the service and/or the application pools run. Make them run under the same non-administrator account you normally use. Then when Visual Studio attempts to attach to the process, the security context will match between the debugger and the process being debugged.
I think you'd only need to change the identity under which your application pool runs.
Here's some more detail from James Kovacs' Weblog: Debugging as a Non-Admin
It looks like that for now, the answer is you can't.
I will delete this if a method or solution comes along.
Is there already a website created within IIS for your project? Writing to the IIS metabase does require admin access. If you setup the website as an admin you may be able to debug it as a non-admin. One thing to try/test is to just point IIS at your website's folder and get it running, then use Visual Studio to do a process attach to the w3wp process.
You could use IIS Express which doesn't require admin privileges. Don't think there's a stand-alone download but you can get it as part of Web Matrix here: http://www.microsoft.com/web/webmatrix/download/