There are designs with just 1, 2, 3, 4 and even, believe it or not, zero spokes out there. As I recall, only the 3- and 4-spoke carbon wheels gained any commercial viability.It's not the spoke count that matters; it is the spoke count and everything else. Gauge, wheel size, style, material, rim, dish flange design, and of course construction details and tension make a strong wheel. If you find the need to true a 36-holer less often than a otherwise equal 32-spoke wheel a fair man might conclude a 36-hole wheel is stronger. Taking away structural material does not necessarily make a wheel stronger (e.g. double-butted spokes). Rather it can improve certain characteristics, but can also adversely effect other characteristics (e.g. stiffness). This is important for some, less important for others.
The modern aero deep dish rims that use 20 spokes (or less) are plenty strong with a low spoke count. But look at those massive (and heavy) rims. The rims are incredible for brute strength and stiffness and simply require less spokes. Now, resistance to rim cracking and longevity seem to be a problem in my shop compared to traditional wheels; so there is a trade-off there.
As for breaking spokes: Properly selected components for intended use and properly built wheels don't break spokes in normal use. They can, with advancing years, but the rims usually wear out first, from my experience. For racing and fun you can always cheat the odds and go a little lighter, but durability suffers.
Yours in Cycling,
North Road Bicycle Imports
P.O. Box 840
166 Courthouse Square
Yanceyville, NC 27379
toll free: 800-321-5511