Personally I am a big fan of jMonkey Engine.Its a shader based & geared toward high end games productions. jGame & Slick2D are very good for 2d games. ligGDX might interest you. All of these are under very active development.
There is no problem in choosing 3d engines for making 2d games. Just ignore that extra D, unless you have some serious issues with that one.
So, I whole heartily suggest you to start with jMonkey Engine, cause its fun, easy to use, has a very active community and comes with an awesome jMonkey Platform which is build on top of Netbeans platform, where every update & features is just one click away. You might end up in using it with many other projects.
There are other libraries too, but they lack community/development activity.
- Genuts - last update 2004
- PulpCore - last update 2009
- GOLDEN T GAME ENGINE (GTGE) - last update 2010
- Basilisk Game Library - last update 2009
You can write your own engine if want to.Then you should use opengl wrapper library, either LWJGL or JOGL. Lwjgl is more widely used then JOGL.