At first it had 4 disks in it, a noisey power supply, a noisey HSF (heatsink/fan for processor), and a case fan.
Step 1 (over a year ago): ditched the 4 whiney disks, moved them to a fileserver and netbooted the desktop. I thought I was done... this lasted me for quite some time. I thought my computer was silent.
Step 2 (last month or so): replaced the power supply with a SeaSonic "Super 300 Tornado" with a single slow 120mm. Great design compared to my old one. Almost inaudible.
Step 3 (last month): unplugged the case fan. Unnecessary. My case never got hot (no insane video cards), and I read most silent computing nuts unplug them anyway.
Step 4 (tonight): just removed the uber-loud HSF and replaced it with a Zalman CNPS6000-Cu copper flower. No fan. Just a beefy heatsink.
So now I just have my slow 120mm power supply fan, which I can barely hear. Cars driving on distance roads are louder.
My computer's slow compared to zippy LJ servers and my desktop at work, but this is wonderful. It's going to be hard to "upgrade" to anything at this point.