NEW! VIA Arena now has a comprehensive guide to Linux on the EPIA, which you should read. Insights into kernels, audio, video and more. Not much about Debian, though.
VIA Technologies has designed some mainboards with the mini-ITX form factor that they call EPIA, EPIA-M and EPIA-V. It's really small, only 170x170 mm.
This site will not go through specs and benchmarks with the EPIA and C3 processor, it is more focused towards helping people with installing Debian GNU/Linux on it, and getting the most out of it.
My system setup
I have an EPIA board with an 800 MHz C3 processor. I bought it mainly for its cool small size, but also for the quiet operation and for building some sort of a multimedia terminal, which will be hooked up to a television. For more information on this project, look at the ninebox pages, that describe the system and the box I've build (or is currently building, or not building).
Currently, I must have overblown the audio-in port with to much current or something. The Linux kernel started complaining about read-errors to the audio chip, and then there are other problems with the BIOS not saving. I'm in a state of "thinking", maybe I'll buy another card in the future.
Update: I got a new 800 MHz card and yes, I bought a new card with a 1 GHz Nemiah processor. So now I have two cards. I used the new one for a while, then I got tired and now both cards are on the shelf - avaiting fun and interesting projects.
Debian GNU/Linux is running on my other computers at home (and at work), so this was my first choice for OS on the machine. The installation procedure is explained more in detail under installing Debian.
There are also a lot of successful stories around on the net about installing RedHat and other Linux operating systems, but not so much about Debian. I find Debian to be easier to maintain and understand, but maybe you'll have to be a bit more interested in computers and technical stuff to appreciate it. RedHat could be easier to start off with.