The folks over at Seeed Studio have been experimenting with building an Arduino-compatible board on flexible printed circuit (FPC) material. Flexible circuit boards are similar to regular circuit boards in that they consist of layers of copper that have an insulator stuck between them. The difference is that the insulating material is flexible, which allows the whole thing to be twisted or bent into a new shape. This might sound exotic, however the technique is used in many commercial products to save space and presumably reduce cost.
The prototype Seeeduino Film isn’t yet for sale, but they are planning to send some units to lucky commenters who come up with an interesting use for them.