koolpianoz.com

This applet allows you to play the piano and will accompany you on different predefined songs.

Needs Java 6 to run properly.

http://koolpianoz.com/

JPL Small Body browser

This applet shows 3D orbit visualization of planets and small bodies (asteroids). This is quite interesting in itself, but especially today, as Asteroid 2009 BD is passing relatively close to the Earth today.

http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2009%20BD;orb=1

madsmx.tripod.com/cannon.html

Cannon Defender is a classic "shoot stuff out of the sky" arcade game, implemented very nicely as a Java applet.

http://madsmx.tripod.com/cannon.html

www.mojang.com/notch/j4k/l4kd/

Left 4k Dead is an applet game written for a Java 4k coding challenge - it is inspired by the Left 4 Dead arcade game, but is implemented as a Java applet, in just 4k, which is a hell of an achievement. It's actually good fun to play.

http://www.mojang.com/notch/j4k/l4kd/

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/