I built a fanless (technically had fans, but only turned on if needed), semi-high-performance open bench-style system several years ago.

It's really pretty nice in theory. The reality is that some components still emit a good bit of noise, and unlike fans, the noise they tend to emit isn't very pleasant. Power-hungry graphics cards are by far some of the worst offenders; without being masked by fan noise, they can be incredibly loud and irritating. An open bench PC is definitely cool, but was kind of a mistake in my case.

Fan tech has improved to the point that I think, more often than not, you really want to have them. Otherwise it's time spent trying to eliminate other noise sources that would otherwise be conveniently and usually pleasantly masked by a little wooshing.