I really like this story on the BBC website, because it's a lovely bit of science. There's a solid that's made of small molecules with lots of hydrogen bonds, which means the molecules hold together well, and if you break it apart, it will stick back together really easily of its own accord.
The obvious problem is water - water sticks to hydrogen bonds very well, so there might be issues if it breaks then gets wet. It would be very hard to dry, and the water might muck up the resticking ability. But there might be ways round that, and it's a very very nice idea.