My Trek FX came with some cheapie 32-spoke wheels that served me well last year, but this year was a different story. Maybe it's because I got a luggage rack and panniers and moved my cargo weight, I dunno. I weigh about 260 and try to ride somewhat gingerly when it comes to potholes and the like. I broke one spoke on the rear wheel earlier this year. Took it to a shop, they replaced the spoke and trued the wheel, then two weeks later the next spoke broke. I had them order me a stout 36 spoke rear wheel with a beefier hub and rim and haven't had any trouble since.
I suspect that the big differences are the quality of spokes and the quality of the initial build. My Trek was a modestly inexpensive bike since I was just getting my feet wet with bike fitness (I suspect a lot of people in this forum are the same way). From what I read, if you have quality wheel components with quality build that it probably doesn't matter how many spokes you have (I went 36h because I was paranoid
). In my situation, I think it was a combination of crappy road conditions, the static weight of my luggage over the rear wheel, and the overall weight of ME. If I'd bought a nicer bike with nicer wheels right from the get-go I doubt I would have had problems.
My road bike (which I admittedly haven't ridden much) has 32h wheels but it has higher quality rims and hubs than my cheap hybrid. I've ridden it much faster than my hybrid and in some similarly poor road conditions and haven't had any problems with it yet (knock on wood).