There have been many releases of Java since the original Java 1.0 release in 1995. (Refer to Java version history for a summary.) However most releases have passed their official End Of Life dates. This means that the vendor (typically Oracle now) has ceased new development for the release, and no longer provides public / free patches for any bugs or security issues. (Private patch releases are typically available for people / organizations with a support contract; contact your vendor's sales office.)
In general, the recommended Java SE release for use will be the latest update for the latest public version. Currently, this means the latest available Java 8 release. Java 9 is due for public release in 2017. (Java 7 has passed its End Of Life and the last public release was in April 2015. Java 7 and earlier releases are not recommended.)
This recommendation applies for all new Java development, and anyone learning Java. It also applies to people who just want to run Java software provided by a third-party. Generally speaking, well-written Java code will work on a newer release of Java. (But check the software's release notes, and contact the author / supplier / vendor if you have doubts.)
If you are working on an older Java codebase, you would be advised to ensure that your code runs on the latest release of Java. Deciding when to start using the features of newer Java releases is more difficult, as this will impact your ability to support customers who are unable or unwilling their Java installation.