Human teeth, that is, not the teeth on the ring or cog. Tim Kelton of Wichita Falls, Texas, was commuting on his singlespeed bicycle when his chain snapped and sent him over the bars. See the gruesome aftermath here. "However expensive that derailleur and a few gears would have been, " Kelton writes, "this is more."
The only time I've snapped a chain is with a dérailleur-equipped bike. It beat my rear dérailleur into little bits before spooling around the rear cog and locking up my rear wheel in heavy traffic, but I managed to stay upright and avoided injury to my teeth or the rest of my face.