Broken spokes are never normal. They're the sign of a crappy wheel build. I ride tandem with my wife and our whole rig weighs about 330 lbs. going down the road. We have never broken a spoke in 7 years of reasonably high mileage riding, including loaded touring over cobblestones. Our wheels are normal 36H bike wheels, but they're properly built.

Added: there are 3 rules for never breaking spokes:
36H
Deep section rims, 25-30mm
Double-butted 14-15 spokes
Spokes tensioned evenly to the rim manufacturers specs