SHAMBLES SOFTWARE
The Fisher Cube, invented by Tony Fisher is a good variation of the regular 3 by 3 cube.

puzzles/fishercube


It's almost exactly the same. The pieces are a different shape which means it jumbles (gets out of shape) when it is mixed up. Four of the six centre pieces are not symmetric so they need to be aligned correctly to complete solve this, which make it a bit like a picture cube. However four of the edges are more symmetric than usual so you don't need to align those, so the difficulty balances out.

The only place you can get these is Meffert's Puzzle Shop.