What do you do if even the smallest Arduino boards (or their clones) are too big for your homebrew project? If you're Johan Kanflo, you find a way to make them even smaller. His AAduino project turns the already miniscule Tiny328 Arduino clone into an even smaller computing device that's about as big as an AA battery. Through creative wiring, it even fits inside a typical battery holder and draws power from the batteries in the remaining slots. He had to underclock the processor to extend to the battery life, but it's otherwise as capable as its normal counterparts.
You aren't about to buy a ready-made AAduino, but you don't have to. Kanflo has posted instructions and schematics both on his own site and on GitHub, so you can replicate his invention yourself. This is mainly useful if you're building an extra-compact gadget (Kanflo needed this for a radio node, for instance), but it shows that even daunting size requirements can be solved with a little ingenuity.