There are 4 game modes to Chuzzle Deluxe - Classic Chuzzle, Speed Chuzzle, Zen Puzzle, and Mind Bender, which is perhaps the most challenging as you have to match the Chuzzles in specified patterns. If you get to the point where you simply find yourself without another move, you can use a limited number of 'Scrambles' which reset or shakeup the board. In addition, some bigger (you could say 'fatter') Chuzzles end up taking up two rows at once which may or may not work in your advantage. These involve puzzle locks that randomly appear and lock the Chuzzles in place.
The only obstacles to your progress are 'no more moves' scenarios.