Most of my sites are running on dreamhost. They’re pretty good for sites running Python, Ruby, or PHP, but they don’t support server-side Java.
Over the years, I have searched for Java application hosting to fill that void. I was mostly looking for a place to explore and try new things, so I wasn’t willing to pay much. The inexpensive ones I found usually had very low RAM, and sometimes shared JVMs between users. To get a private JVM capable of running a decent app server usually cost more per month than I was willing to spend, and often required a dedicated server or VPS, which was more of a time commitment than I wanted. Eventually, I stopped looking.
At some point Google came along with their App Engine. It allowed part of what I was seeking, but came with its own limitations.
Today I discovered OpenShift, though it appears to have been started two years ago (May 2011). In additioon to Java, it supports a handful of other languages, as well as an assortment of frameworks and databases. It has a free version that is limited, but even the free version appears to support JBoss and MySQL!