Libertango, the 2009 version
Zotac ION ITX B motherboard, Silverstone SG05 case, Scythe Slip Stream 120mm fan, Be Quiet SFX power supply, SSD.
The SG05 came with its own fan and PSU, but they were too noisy. The configuration above has two fans, but is very nearly as quiet as the previous libertango (a fanless hush box) and (update:) much more resistant to summer heat.
The only negative aspect is that the LEDs are bright enough to read by.
Update: On advice of buzh, I painted over the power LED with a black Posca pen, which dimmed the light to a just-visible level. The HDD LED hasn't bothered me since I unplugged it from the motherboard.