Any advice about how to build a cheap and fanless server? It's main uses would be web and file servering, but it could be a day when I'd like to add some streaming and mailing capabilities as well.
OS of choice: GNU/Linux
Take a look at Atom powered devices. Atom N330 should be powerful enough to do most of the home server duties, and it is relatively cheap and consume just a bit of power. Not to mention that it doesn't take much space either.
I'd look especially at Acer Revo R3610 but there are completely fanless models available.
You can see many references at Silent PC Review. They're more concerned with eliminating noise, not minimizing cost, but you can pick and choose from what's available.
I don't know your definition of cheap, but a Pogoplug may just fit the bill.
I have an Intel D410pt motherboard (bearing a D410 "dual core" atom processor at 1.6 GHz), hooked up with 2 GB of RAM and a 160 GB 2.5" hard disk, for about 130 EUR, which isn't much. It can run fanless, but because of the location I'm using it in, I had to put in a fan sadly.
It's running on Arch Linux 64 Bit, hosting an IceCast streaming server, a network storage file system, FTP and HTTP without any problems!
Looking into Atom based devices might be a good idea :)
Easily build a comprehensive server with free integrated software applications incl email, streaming etc. Very well described at www.ulverston.myzen.co.uk/mini-itx/index.htm
Try this hardware bundle www.mini-itx.com/store/?c=38
The motherboard has onboard SATA RAID facility as well as two IDE connectors.
NB: no FDD connection so use USB floppy if required.
Make sure they send the NEW PCI Wi-Fi Card (prob not needed for this project, but useful).
Motherboard Documentation from manuf site.