Update (7-30-10): Claudio Baiocchi notes that in 1964, James H. Caldwell found a dissection of the 12×12×12 cube into 8 pieces and this is the best possible. A graphic of his dissection is below (Piece A is the 9×9×9 cube, Piece I is the 1×1×1 cube and the decompositions of the 12×12×12 and 10×10×10 cubes are shown in layers.)