The 'Anaconda' or 'Snake' pattern has a path, winding from face to face until it overs all six faces of the cube. I like it for two reasons. One - it has this nice unusual symmetry. Two - it's hard to make.
The video below shows the simplest method of doing it. You do a sequence of apparently random moves, turn the whole cube cube, then 'undo' the sequence. Enjoy!