A couple of hints to get you started...

Movie at the bottom of this page

The Checkerboard - 8X8
The 'puzzle movie' as seen at the bottom of this page shows the formation of two 4X4's -
These also form the 4X8 and the 2X4X4 ...
HINT: Two 4X8's can also form the checkerboard and the 2X4X8

The Challenger - 1X6X6 (only 1 possible solution)
Solved by Abel Garcia
HINT: The 'H' doesn't work in a 6x6 grid ;-)

The Super Challenger - 2X5X6 (only 1 possible solution)
Solved by Dave Hecker
HINT: As with most shapes, you can calculate the piece 'NOT' to use. Since the total cubes for this shape is 60 and only 2 pieces have 4 cubes each it is just a matter of logic to figure out which piece is not part of the shape since dark and light colors must match.