My mobile PC is a VIA Mini-ITX board with a VIA C7 Processor running at 1.2 GHz. This processor is basically an i686 running on very little power.
The board is combined with a Car/mobile PSU rated at 60 W accepting 6-24 V DC as input.
As mass storage I currently use a 80 GB Notebook HDD which will be replaced by some sort of Flash memory,
Together with the CPU hard at work the Computer manages to draw about 25 W or about 2 Amps from the battery pack (12 V, 28 Ah) of rechargeable lead gel batteries.
Additionally to that there will be an 8" touchscreen on it to be able to directly interact with all necessary processes of mapping on the move, and this, too, runs on 10-15 V DC, and thus can be powered by the same battery pack as the other hardware.
On the bike it's currently not connected, until I find a good way to fix the screen to my bike while protecting it from excessive g-forces.
Currently I'm running Gentoo Linux on this box, and use this as cycle navigation and osmapping platform. The software of choice will be GPSDrive or Mapper if and when I can get it to work with the touchscreen.