Do you mean the lug NUTS broke, or the lug nuts fell off, or the lug BOLTS (actually, on almost all cars, studs, but never mind that) got sheared off?
Lug nuts fall off because somebody dodn't torque them and they gradually unscrew themselves. BTDT and had that done to me. If you're really lucky, all five can go, at which point one corner of the car gets all low and loud and sparky a la "America's Wildest Police Chases."
The various means by which the lug bolt could shear off include massive overtorque (e.g., the "get the stand on the handle until it squeaks" school of torque estimation) or simply trying to bust something really tight using the L shaped lug wrench thoughtfully provided by most car makers. Between its shape and the wretched body position involved in changing a tire, it's a marvelous tool for applying axial bending moment as well as torque to the lug bolt, especially for the inexperienced. They're not really made to bend -- they snap before too awfully much of such mistreatment.
Never saw anybody actually break a lug nut, though I suppose enough torque (or a hidden flaw) could do the trick.
--Joe