I fall into the category of 'Nerd' so here's my 3 Euro's worth.
Inexpensive tends to equate to 'slow' unless you buy used. There are handful of people who have run WCG on Intel Atoms (netbooks), myself included, and they do eventually turn in results.

One suggestion (there will be others) The later Intel Atom CPUs benchmark (passmark) at about twice the rate of the 2004-ish Pentium 4 3Ghz chips, and the current (affordable) queen of Atom motherboards will have a D2550 on it, or at least a D2500. They're not cheap, but boards like the charming Intel D2550MUD2 are asingle board PC with DVI/VGA graphix which do crunch a lot of work at very low power.

They benchmark (Passmark) at about 674 and have a Tdp of about 10 watts, so they can run from solar panels, and boot from USB sticks. They'll run Windows 7/8 or Linux quite happily and are passively cooled but still require forced airflow for 100 per cent 24/7 crunching.

With a 2.55" SSD, 2GB of RAM they pull around 13 watts at 100% on both cores.

I have one awaiting set-up, and will post some results next week.

However, as others have pointed out, getting work done on slow CPU's might mean work units cannot be delivered in the timescales required at WCG, possibly a case with the Raspberry Pi. The early Celeron CPU's in the Asus EeePc701 were capable of around one work unit per week.

If you want smaller, faster, and more expensive there's the Intel NUC.

Apologies for the many edits. People keep interrupting me and asking me to 'work'.

Un-besmirched by practicality, impossibility, common-sense or logic, R-Pi's can Boinc and look for aliens in the skies.

http://burdeview.blogspot.co.uk/p/raspberry-pi-boinc-project-ive-created.html

Should this not be enough, it appears that the danged things can be over-clocked.

What next? Running Windows? :-)

I would agree that the research teams behind the projects will have to look long and hard at whether compiling for ARM based systems will be worth it. However, with continuing developments in the field and changes in computing trends it is something that we should definitely be keeping an eye on and not dismiss out of hand...especially when someone comes up with something like this:

http://www.southampton.ac.uk/~sjc/raspberrypi/

Anyone for a low(ish) cost supercomputer?

I think that some research might be usefully done to investigate Rasb-pis, Atoms etc, maybe clustered?

Though the Atom has the edge of being WGC 'compat' out of the box.

The first valid results are back, so far so good. It did take '14 hours 7 mins' to crunch an HCC WU, which is not remotely fast, but at the same time, it was crunching 3 others for its 30 watts at-the-wall consumption. (Ubuntu 11.04 32 bit, 4Gb SODIMM, 250 Gb 2.5" drive). This is rather more than the 10 watts MAX TDP of the D2550 CPU

But, of course, there's a cost to Rasb-pis and Atom boards, I agree that the money might be better spent (for WCG) on a GPU? Of course, for a 'novelty' low power machine, the fact that it produces useful work at all is good news. A pity the embedded on-chip GMA GPU cannot do any work

(How about a Linux Rasb-pi running WGC/Boinc under Wine?)

Here is the er, mighty Atom crunshing for WCG on my desk:

Ouch,
Now I've replaced my old server by a RPi, and can not contribute to WCG anymore with boinc 'cause not compiled in armhf :s
May be there's another program who can connect to WCG and can make contribution to, with RPi compatibilities ?