The very simplest answer is that licensing is required if you are not using Java for the purpose of using it to run another Oracle product/technology. If you are using it for your own home-grown application running on a non-Oracle server (or running locally) then licensing is expected. To get the official feedback refer to the published documentation. If that doesn't answer your question clearly, please contact Oracle Sales so they can review your exact circumstances.
Here are some helpful resources:
Those links seem to be in regards to Java SE. The original post and question is about the Java JRE, which as I understand it, is a completely different product.
I could see Oracle wanting to supplement the income stream by charging people a fee to have the Java development environment, since they in turn churn out the software that they charge money for. So sort of like if Microsoft started charging money for people to use one of their compilers.
But as I understand it (along with millions of other people), the JRE is the "Java Run-time Environment", so more along the lines of say the Adobe Acrobat Reader. The Reader is free, but if someone wants to create or edit PDF's, they need to pay for the software to do that.
Is it really Oracle's intention to start charging every person in the world the sues the run-time environment to run somebody else's program? Seems like a real good way to kill Java if that's the case. But then again, I was saying this would happen when Oracle first announced that they had "acquired" Java and it's licensing from Sun, but insisted it would always be free to use, but maybe not to develop.