I think it depends on what you kind of games you want to create? Do you want 2D or 3D? Hardware accelerated or not? Puzzle or action? Network?
Each of the above decision will affect how you create your game. For example, if you want a simple 2D applet game, you will want to use the swing Canvas class and use the Graphics class to draw and paint stuff on screen. If you want OpenGL hardware accelerated games, you'll want to look at OpenGL bindings like LWJGL or JOGL. If you want hardware accelerated but don't want to deal with low-level OpenGL calls, you'll want to look at game engines such as Slick (for 2D), and JavaMonkeyEngine or JPCT (for 3D).
There are so many choices that it is very easy to get confused when you are just learning the basics of game programming. Since I teach java programming and I have an interest in 3D accelerated games, I have created my own framework specifically to make it easy to learn the ins and outs of programming concepts in a gaming context. You can find the tutorials at http://env3d.org
. The lessons are very easy to follow especially if you are a professional Java programmer.
Good luck and have lots of fun!