This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
There are basically 4 different API's you should look at.
JOGL - Simple wrapper around opengl functions that is geared towards any kind of opengl development LWJGL - Simple wrapper around opengl functions that is geared more towards gaming jME - 3D Scenegraph based gaming engine. Currently uses LWJGL for opengl function calls Xith3D - 3D Scenegraph based gaming engine. Looks a lot like JAva3D. Currently uses LWJGL or JOGL for opengl function calls.
Each site has detailed instructions on how to get started using their libraries.