Start simple, think Atari 2600. Games like pong, space invaders, pitfall, etc. This should teach you some basics like the game loop, drawing, collision detection, and input handling while avoiding more advanced areas like path finding and AI.
I personally learned a lot from the book Killer game programming in java, and the java doc. I have seen the slick space invaders tutorial linked a lot here but I haven't read it so I can't comment on it.
Killer game programming in javahttp://fivedots.coe.psu.ac.th/~ad/jg/