MAKE Flickr Pool member Funax made an Arduino-compatible board powered by a single AAA battery.
A step-up converter is used to boost the battery’s 1.5V output to 5V and meet Arduino’s minimum power requirements. Keep in mind – this circuit would considerably reduce current supplied to the board and therefore limit its ability to power external components.

AAArduino on Flickr- Link
Learn more about DC-DC converters on – Link

Uduino – Low cost Arduino development boardLink

Arduino @ MAKE – Link