Does an asp.net web-server run a new instance of a web application per request?

The app domain is constant (can be recycled) and is created only on the first request (also can be set before that).

That is to say all the static variables are initialized only once but all the not static classes on which your request depends are initialized on every request.

So basically all your pages in normal asp.net and all the controllers in asp.net MVC are initialized on every request.

read more about it here http://www.codeproject.com/Articles/73728/ASP-NET-Application-and-Page-Life-Cycle

*note - the image has been take from the article referred above