E.g. the AMD Turion MT-37 is rated at 25W (TDP), though only single core. The AMD "3800+ EE" is around 40W (if you undervolt), however it is dual core. The Turion TL-52 is also dual core and rated at 31W, however it is Socket S1 and good luck finding a mobo for it.
I'm not sure about Intel C2D's. A buddy of mine just bought a sweet Toshiba laptop with an Intel® T5500 Core™2 Duo processor. Rated at 34W. Not sure what socket is used but it runs on the 945 Chipset Family. I hear rumors of an Ultra-Low-Power C2D in the wings, i.e. 5-10W.
N.B. Even though these are low power CPU's you'll still probably use a high-quality heat-sink, e.g. Zalman CNPS 9500 or Scythe Infinity.
Get a good case. Then think about getting an 945 (Intel nomenclature) Chipset based mobo, e.g. Gigabyte GA-945P-S3 or GA-945PL-S3 or Epox EP-945 Pro. Get a good heatsink, e.g. Zalman CNPS 9500 or Scythe Infinity with a Nexus 120 fan (or better). Run without the fan -- but watch the CPU temps closesly -- or run with the fan at the lowest RPM. Use Sound Dampening materials in your case to quiet the fan, if you run it. Check out http://www.silentpcreview.com/ for more ideas along those lines.
I'm outta time. Gotta run.
Btw, how are you using the computer? Is it for an entertainment PC, or a desktop, Enterprise desktop, mobile, small business, etc. ?