I’ve been unhappy with PC noise for years, and tried a variety of things to cut it down. I find it tiring, distracting, and just plain annoying. Thanks to a few recent innovations in hardware, though, it’s now easy to put together a nearly-silent PC, fairly inexpensively.
I’m a huge fan of the mini-ITX boards and cases. VIA dominates with its fanless chipsets, they come with everything you need built in (audio/video/LAN) though it’s not high-end quality, but totally workable.
The good part is that there are no fans required on the CPU or the case, if you put it together with the right parts. No fans and a quiet drive = near silence.
The basic ingredients are:
- VIA Eden ITX mobo (make sure you get one of the slower, fanless ones)
- One of the 2677 cases that have an external PSU (check out directron, etc.)
- The Seagate Barracuda IV drives with Fluid Dynamic Bearings (I use the 80′s)
Unfortunately the little cases take slim CD drives, which are pricier. I haven’t tried using a drive enclosure here because I don’t think it would fit, and the noise level is so low anyway it’s fine.
You don’t need to do much more than screw them together carefully, attach cables and go. You will need an OS to install 
Here’s my (somewhat aged) list of links for quiet pc products and articles:
http://www.zalmanusa.com/
http://www.sharkacorp.com/
http://www.casetronic.com/Product/PCcase/2677/CS-2677.html
http://www.computergate.com/products/item.cfm?prodcd=B7VEPIA8
http://www.siliconacoustics.com/tkpow300wfan.html
http://home.swipnet.se/tr/silence.html
http://www.neoseeker.com/Articles/Hardware/Reviews/silentpc/
http://www.siliconacoustics.com/
http://fredrik.hubbe.net/silence/how.html
http://www.quietpc.com/cgi-bin/order1.pl
http://www.directron.com/silence.html
http://pmitros.mit.edu/silence.html
http://www.directron.com/612ngmi.html
http://www.ocshoot.com/quietpc.htm
http://www.nwccomputers.com/silent.htm
http://www.pcpowercooling.com/ordering/index.htm
http://www.4p8.com/eric.brasseur/cnoise.html
http://www.directron.com/xtreme.html
http://www.d-silence.com/reviews/silencer.shtml
http://users.ev1.net/~redelm/
http://photos.sonicspeedsters.com/tardis/
http://www.makeitsimple.com/projects/case_noise/index.shtml
http://staff.washington.edu/gray/silentpc.html