If your CPU horsepower needs aren't massive, Mini-ITX is the way to go. I've recently put together 1U devices for a firewall and a general purpose/file server, and an Asterisk box is on the way. It's hard to beat this form factor for low power consumption, which of course translates into less heat and less noise. The downside is usually cost--Mini-ITX motherboards tend to carry a price premium over their larger counterparts, as do the mobile CPUs which often go with them.
Cases aren't hard to come by; the SuperMicro cases recommended by others seem nice, and while not designed around the Mini-ITX form factor, will probably work nicely with such motherboards. However, I've found that iDOTpc (http://www.idotpc.com) has some nice and (relatively) inexpensive 1U rackmount cases in 8", 12" and 16" depth at very reasonable prices. The 8" and 16" models can be configured without a power supply if you intend to provide your own (as some Mini-ITX boards include onboard DC converters and use an external brick).
Then you just need to choose a motherboard that fits your needs. For the firewall I used a PC Engines ALIX.2C3, which is actually not Mini-ITX form factor (it's slightly smaller), but which fit in the aforementioned iDOTpc 8" case with little modification (I had to add some standoffs at appropriate locations and cut up a generic I/O backplate). There are several models in the ALIX family--with varying amounts of network ports, mini-PCI slots, etc.--all of which consume 5-6 watts of power when active. (Incidentally I got mine from Mini-Box.com, http://www.mini-box.com).
On the other end of the power spectrum, there are boards that can use mobile dual-core processors from Intel or AMD. I went with an AOpen i945GTt-VFA, which is an Intel Socket M board, into which I installed a 1.66GHz Core 2 Duo. Coupled with a pair of SATA drives in iDOTpc's 16" case, the system uses about 40W when idle and perhaps 50W under load. Of course this doesn't run fanless; in addition to the CPU fan there are two case fans (also supplied by iDOTpc) rated at 24.0dBA. The system is still very quiet, especially since the fan speeds vary with the system temperature. Incidentally I procured the i945GTt-VFA from Logic Supply (http://www.logicsupply.com), although they don't stock this particular board anymore.
There are plenty of other Mini-ITX boards to choose from, with varying amounts of CPU power, I/O capability, power consumption and of course price tags. The most common suppliers seem to be VIA, Jetway and MSI (and even Intel, which offers a very inexpensive board, which unfortunately isn't suitable for 1U installations). And Intel Atom-based motherboards are (hopefully) just around the corner; it will be interesting to see what sort of performance-per-watt they will provide.
Finally, don't let anyone tell you that you shouldn't use a rackmount form factor. Sure, it might end up costing a little more than using desktop parts, but there's a certain elegance about it. It usually doesn't make sense to drive old British sports cars, either, but I'm sure those that do, understand. :-)