We have an old page written in Classic ASP that makes calls to an existing .asp page through the Prototype library's Updater object.
This call passed some query string parameters in w/ the request and received a list of params to update as well as a block of HTML/JS to render onto the main asp page.
It seems that the page lifecycle complicates things, but implementing in an actual server control or usercontrol could work.
[EDIT] I'd like to clarify/simplify the original question: Is there a way to render an ASP.NET control (.ascx or server control) in a non ASP.net page?
Ideally it would be called via AJAX and return a block of HTML Text - along with some way to transfer state to the receiving page.
You could place the control in a web service that returns the raw HTML as output and call the web service from AJAX placing the results wherever you wanted using dynamic HTML. You might have to play around with the output buffer of the control to get this to work the way you want it though.