Amazon's Elastic Beanstalk is a good compromise in this regard. I've been using it to develop some JRuby/Sinatra backend services, and though it's not quite as simple as Heroku, it's pretty close. Since the applications are just EC2 instances underneath the hood, you can tweak the server image quite a bit too, which is nice when you need to run some odd binary programs along side your web application. I haven't played around with Beanstalk's autoscaling feature yet, but that might come in handy for processing background jobs that fluctuate a lot.
If you want "here is a war file" then aren't you looking for beanstalk and appengine?
Cloudfoundry as well.
Don't you get that by FTP'ing your WAR to Tomcat, whether running on a dedicated server, VPS or in the Cloud, or am I missing something and overly complicating my life?
You're missing the bit where you run Tomcat on a VPS. Deploying RoR isn't much more complicated, but still infinitely more complicated than dropping it on Heroku and having it just work. Plus scaling: breaking a sweat on Heroku? Push a button. On your VPS? All kinds of trouble, just when you probably have other things on your mind.
Try Cloudbees for that. Plus they do continuous integration with Jenkins as well.