This week's book giveaway is in the OCAJP forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide 1Z0-808 and have Jeanne Boyarsky & Scott Selikoff on-line! See this thread for details.
As a bean provider, you can and should always wrap checked exceptions that the client is not expecting (not declared in your interface) in an EJBException, and throw that EJBException. You don't have to declare the EJBException in your home or component interface. The compiler won't complain...
If your business logic encounters runtime exceptions, just let them propagate to the container.
I'm not really sure the specs allow you to declare runtime exceptions... anyone else ?
If you create your own application exceptions, they should not extend RuntimeException or RemoteException. You need to declare those application exceptions in your bean class and your home or component interface if you throw them.