One of the questions I get asked about like clockwork when I do Virtual Earth programming sessions to government customers is "How do I get my 'ESRI data' onto the map?"  I always caveat that I don't know much about ESRI products.  I then tell people that Virtual Earth is a platform visualization of data on a map.  It is not tied to and does not dictate the data you visualize.  I always tell people that if you have the data and can expose it to the client, then you can use the APIs in the v4 Map Control to create your own tiles, draw lines, polygons, routes, pushpins, etc.

None of this really answers exactly HOW to do this.  I usually recommend exposing the data through ASP.NET Web Services and using ASP.NET AJAX 1.0 to make them callable from JavaScript (see tutorial and video for more details).  This makes it really easy to get the data from the server and then use the v4 Map Control to visualize it.

As I understand it, this can still be quite a bit of work to ultimately surface your "ESRI data."  I recently learned that a Microsoft partner, ISC Consulting, has a product (built on ASP.NET AJAX 1.0) called MapDotNet Server 2007 which makes this task much easier.  Coincidently, the Virtual Earth for Government blog just posted a Virtual Earth for Zoning Applications entry which talks about this as well.

DISCLAIMER: I have never used MapDotNet Server 2007, nor do I have any existing relationship with ISC Consulting.  This is not an endorsement of their product.