Update 2021-09

• For versions 8 through 16, Oracle required a fee if their own Oracle JDK product was used in production, but not for dev, test, and training usages.
• For Java 17, the Oracle JDK product is available under a new
  No-Fee Terms and Conditions license, discussed on the Oracle
  company blog.

On my first reading, it appears this new license makes production use free-of-cost (along with dev, test, and training usages), except for products sold for a fee while bundling the Oracle JDK product. But I am not an attorney, so read the terms yourself and consult legal advice as needed.

Keep in mind that many other vendors continue to provide implementations of the Java specs, as shown in the flowchart below. Some of these vendors sell support plans, either optionally or as a requirement for use of their product. Never assume, always read the detailed requirements for any distribution you obtain.

Another 2021 update: Add Microsoft to the list of vendors seen below.

Several vendors offer a choice of Java implementations

The Answer by Speakjava is correct and informative.

In addition, here is a flowchart I made to guide you in choosing a vendor for a Java implementation.

Or another way to view this: Your particular motivations or situation.