The Arduino Uno microcontroller prototyping board can run off power ranging from about 7 to 12 volts, converting it all to 5 volts and 3.3 volts for the components on the board. When you connect an Arduino via USB to your desktop system to download software, it can run off the 12 volts provided over the USB cable, just like a keyboard or mouse. But you can also run it off the ubiquitous wall wart in the right voltage range with a 2.1 millimeter center-positive power plug.
Or you can go by Radio Shack, spend a couple of bucks on parts and a few minutes with a soldering iron and heat gun, and make a mobile 9 volt power supply.
Add to this one of the tiny Zigbee radios I've been writing about as part of my Amigo project and you have a self-contained wireless computing platform. Zigbee was designed from the ground up to be a personal area network (PAN) technology with short range (a few hundred feet) and low power (about a milliwatt). Zigbee radios come in three personalities: coordinator (a.k.a. ZC), router (ZR), and end device (ZED). The first two have to be powered up at all times in order to manage and route messages for the mesh network. But end devices can spend most of their time powered off; the other personalities will store and forward any packets destined for an end device when it periodically wakes up and connects to the network.
It pays to think small.
I haven't measured yet how long a 9 volt battery will last, but it's not that long. Here's another approach that provides 12 volts for longer duration than the 9 volt solution: eight 1.5 volt AA batteries in series in a battery pack. The pack from Radio Shack has a 9 volt battery connector on it, so it's trivial to switch from the 9 volt battery to the 12 volt battery pack. Here's the pack powering an Arduino Uno with an XBee radio shield transmitting to my desktop system.