Rubik's 2x2x4 Tower
This puzzle was designed by Hidetoshi Takeji, inventor of the Bump cube and several other interesting puzzles. This puzzle allows quarter turns of the long faces and results in a shape-shifting puzzle.
This is an interesting puzzle. It isn't that hard to solve using algorithms that you might use on all sorts of other puzzles. The extra layers mean that some of the algorithms you'd do on a slim tower or domino produce effects that you might not have expected but the quarter turns allow you to bring in all sorts of other algorithms that make life a little easier.