OpenJDK builds from AdoptJDK [1] have LTS versions. The also state the following in their Roadmap [2]:
In addition, every three years one feature release will be designated as the Long Term Supported (LTS) release. We will produce LTS releases for at least four years. This assurance will allow you to stay on a well-defined code stream, and give you time to migrate to the next, new, stable, LTS release when it becomes available.
But they're not major versions. Java has switched to "Chrome versioning," and every new feature release gets a new number. Those versions are supported until the next one comes along.
To expand: in the waning days of Sun, they open sourced large parts of the Java development kit (JDK). This became OpenJDK, and is GPL v2 licensed (with a linking exception).
Initially, not all code was available under a GPL license.
Separately at the same time, Apache led the Harmony project to produce an open source implementation of Java SE 5 & 6. This was successful.
As time passed, Sun (and maybe Oracle) open sourced more code into OpenJDK, leading to supporters switching from Harmony to OpenJDK. Additionally, Sun made the unfriendly move of licensing the TCK in a way that precluded any non-OpenJDk release from ever being able to claim Java compatibility. In response, Apache resigned from the Java board. And as of 2011, the Harmony project was stopped.
Because of the platform-independent goal of Java, there's a lot of ancillary "not-Java, but needed" libraries to build and run Java. These were not all open sourced by Sun / Oracle, but were reimplemented by RedHat under a project called IcedTea.
So, in summary, you can run OpenJDK/IcedTea and tell Oracle to pound sand.
The primary risk is that Oracle withdraws the things they do still control from the OpenJDK project, or stops working with the project to coordinate new releases. But they'd be shooting themselves in the foot if they did.
Working with the project to coordinate releases? Oracle employees run and manage the OpenJDK project (which is owned by Oracle, BTW), and contribute ~90% of the work (including designing future releases):
