I'm surprised that nobody's suggested a netbook yet. I bought a refurb Asus Eee 900a for about $150 (woot has them pretty frequently, although I got mine from mwave) and then maxed out the RAM and SSD for about $50 more, taking it to 2GB RAM and 16GB SSD. It has a 9" display that I have set to turn off when I close the lid, but even with the LCD on max brightness it only draws around 12 watts.
There's a SD card reader built-in that you can install linux from, or use one of the USB ports. You could hook up an external drive or use the SD card slot for additional storage, but since all I'm doing is network services (ssh, http, tinyproxy, etc) the storage isn't much of a concern. Going wired instead of wireless would save some power as well.
Best of all, it has it's own built-in UPS
I evaluated taking a consumer NAS device and repurposing it, but the hardware specs you can find in a comparable price range aren't nearly as good (except for the drive, obviously). The SheevaPlug is interesting, but it is nice to have a display and keyboard integrated. It makes for easier setup and debug when something is going wrong. Plus, at the time, they were in short supply.