if you want a flash like experience with java applets, then theres no better library to use then PulpCore
http://www.interactivepulp.com/pulpcore/ an example game can be seen here
http://www.pulpgames.net/milpa/if you want powerful and fast 2d games with Java then use the Slick2D library
http://slick.cokeandcode.com With Slick2D you can create standalone games as well as applet games, it also has a great community.
if you want a light 3d engine which works reasonably easily in the browser, JPCT is the way to go
http://www.jpct.net an example JPCT game can be found here
http://www.cokeandcode.com/applets/jpctIf you want powerful 3d games with java on the level of modern 3d AAA titles, then jME
http://www.jmonkeyengine.com or Ardor3d
http://ardor3d.com are the libraries to use.
If you want to go old school and have direct access to low level libraries like OpenGL and OpenAL then LWJGL is the biniding to go for
http://www.lwjgl.orgJust my opinion.