Floppy Cube (3x3x1)
This puzzle was invented by Katsuhiko Okamoto, who also produced the slim tower and the void cube. Like many of his puzzles, it seems impossible until you get to use it. The puzzle on the left is a genuine floppy cube. The other puzzle is a shape-changing variation that also allows you to twist the edges that you have to solve on the proper floppy cube.
It is very easy to solve this thing. Mess it up, do what you think you need to do to solve it and there you have it. Not the greatest challenge in the world, but such a lovely puzzle that it's very hard to resist getting one.
The genuine floppy cube is sold by Meffert among other suppliers.