Don't like fans? No problem, as long as you REALLY like heatsinks...
I saw an outrageous case over at Gizmodo - this guy custom built a case for his computer out of aluminium heatsinks.
That's right, the whole case is a heatsink.
Copper heatpipes are used to transfer the heat from the heatsink on the processor, and everything is mounted on monstrous open air heatsinks. Cool to look at, and it would be quiet, but I bet its a dust magnet.