I recently came across Heroku, which looks extremely cool. You just upload your app and you're done; it scales without further intervention. Unfortunately, Heroku is for Ruby and our app is in Java.
It's a webapp, implemented as a .war file. We want it to scale automatically across clusters of servers maintained entirely by other people.
We've spoke to Rackspace. They have "Rackspace Cloudsites" which does this for Wordpress. They have no intention of supporting Java app servers in this way.
What else is out there?
Take a look at Google App Engine. In your case, the App Engine Java Overview will be helpful. You can also build App Engine applications using Python.