Uwe Meffert's puzzle site. Uwe has all the best twisty puzzles for sale at low prices, full solving instructions for each (even the 5x5x5 cube), and interactive Java applets. I unhesitatingly label this site as a BEST OF FIELD. It is closely affiliated with David Byrden's Twisty Puzzles, which is the best Twisty Puzzle Java site I have ever seen.
A four dimensional Rubik's Cube is available from Daniel Green and Don Hatch. It's a very pretty program... I can frequently undo 5 moves (beat that!).
Moves for the 4x4x4 and 5x5x5 cube can be found at Mark Longridge's and Jake Olefsky's site.
GAP, short for "Groups, Algorithms, and Programming", is a free, downloadable program that can solve large problems in Group Theory. The opening example of this program shows how to use GAP to calculate the number of positions in a 3x3x3 Rubik's Cube.
Rubik's cube and its variants has many solutions and applets.
Tico and Teco are Rubik's Cube solving robots. This site has many Rubik's Cube links, and pictures and animations of the robots doing cube solving.
Solving Rubik's Cube by David Lee Winston Miller shows a nice heuristic method.