Instead of using a PC, or even instead reusing a consumer device, you may also create your own system using dedicated embedded system boards. Because of lower volumes, such boards may be a bit more expensive, but they can achieve much reduced size and power consumption. Both low and higher volumes are available too.
Here are a few noteworthy examples:
Picotux - The smallest Linux computer in the world, only slighly larger than a RJ45 connector. Pretty cheap too.
Gumstix - Small, affordable embedded boards with the size of a gumstick. Backed by an active community too.
See this independent list of interesting board suppliers for more details.