The JBoss AS was renamed to WildFly. The latest stable version is 9.0.1.Final. Please see WildFly Homepage · WildFly for more details.

I think this depends on how you define a 'stable version'?

All versions published on the WildFly download page should be stable versions WildFly Development - Moving component projects to a "feature pack" model?

Also alpha and beta releases are stable and may be used. But there might still come major corrections or even functional changes before the version is finally released.

Final releases are stable versions in so far that you should not expect major changes any more but there might still come some minor corrections (mainly caused by bugs). 

If you use Infinispan for caching you might switch to the new release of infinispan and use the WildFly modules of ISPN to be able to use a newer version of if, also the modules might contain more features as the infinispan subsystem in WF might not have the full functionality.

If you want to use a 'stable' version you can use the downloads on the WF page, the release should collect fixes and it is ensured that the server pass the tests. from the git repo it might be not always the case.

If you need a more relyable and better tested version you might use the EAP/JDG bits, here you don't have the latest features but it is better tested but with a subscription you get fixes for your version a longer time. whereas you have to use the latest WF version to get fixes or you need to backport it by yourself.