a very noob question. Can I run a .jar file on Tomcat. I am not building a web-app. I simply need to run a .jar with say HalloWorld in it. Is this possible/appropriate.
I don't really know what your use case is, but what you probably need is a virtual private server (VPS) provider. They give you a virtual host which runs OS of your choice and you can install JVM on it. There are many VPS' available. Try Linode or Slicehost.
It would help if you would explain what you are trying to achieve, then we might be able to give you a better answer.