This page describes some of the problems that I ran into getting the bindings to work under Debian GNU/Linux 2.0, with the Blackdown 1.1.7-1a Java port. If you are using a later version of Debian or the Blackdown port you should have no problems. My current work environment, which consists of Debian 2.2r2, JDK 1.3 and the NVIDIA OpenGL drivers, is problem free.
You'll need to have Mesa or some other OpenGL implementation installed on your system before you can even compile the bindings. However, you have to be careful about how you compile Mesa if you want to write a multi-threaded Java application. Since it's almost impossible to NOT write a multi-threaded Java application, you probably care, even if you think that you don't. I recommend Mesa's linux-386-pthread-shared configuration.
The Debian Mesa package doesn't appear to have been compiled with threads in mind. That means you'll have to get and compile Mesa on your own, if you want things to work properly. It is also important that you use the native threads package that comes with the Blackdown distribution. I've ran into Mesa problems that were caused by mixing green threads with native threads.
You can test things out with the Concurrence example inside the test directory. It will try to open up two windows, and then try to perform some animations in both at the same time.
Earlier versions of Mesa did not have the latest and greatest GLU functions (it now does). Use of unsupported functions will result in an UnsupportedMethodException being thrown.