I have always enjoyed peg solitaire. The goal is to remove all the pieces from the board. You remove a piece by jumping over it on to an empty tile. You cannot jump diagonally. Simple rules but a difficult problem! I wrote my own version of the game which you can play below (might take some time to load).
The game is written in Java using the excellent (but now defunct) PulpCore library. PulpCore gives me lots of shiny effects for very little development effort so I had a lot of fun putting this toy together. You can grab the source code from my Mercurial repository. I also created the art for the game. It's adapted from High King but I had to redraw everything for its new size.