turbulence.org/spotlight/thinking

The Thinking Machine is a Processing based applet that will give you a good game of chess, but the cool thing is that while it is thinking about its next move it shows you the potential moves that it is considering, using coloured lines.

http://www.turbulence.org/spotlight/thinking/

http://www.processing.org/

Thanks to Rex Guo for the tip.

metamolecular.com/chemwriter

This is an applet that allows you to design chemical structures in a WYSIWYG editor. The editor supports undo/redo, importing and exporting of diagrams and it can be controlled by JavaScript. I know nothing about chemistry, but the diagrams look convincing to me :-)

http://metamolecular.com/chemwriter/

allstarpuzzles.com

This site has a collection of pen and paper puzzles, such as anagrams, Sudoku, and spot the difference (pictured), all implemented as Java applets.

http://allstarpuzzles.com/