Take a look at OpenShift.com.
https://openshift.redhat.com/app/
You can deploy applications to JBoss AS 7.
You are given 1,5 GB RAM and 3 GB of space.
You can have MySQL, SQLite, PostgreSQL, MongoDB...
You can have Cron scripts.
You can connect anywhere from the server.
You get SSH access (not root, though).
Definitely, give it a try.