Happened to me once when I over-tightened the bolt on the knuckle joint of an adjustable stem - I was trying to stop it creaking so in my ignorance and inexperience I tightened it 'extra-tight' (I've since learned (the hard way!) to grease it liberally instead) and - unknowingly, of course - sheared the bolt...
Rode down to the town on a busy 60 mph single carriageway (no cycle path then; there is now, even though it's bordered by a hawthorn hedge and it's unusable for half the winter when they cut the hedge, but that's another story) on a Saturday afternoon with nothing holding the bars on except two ends of a broken bolt, until eventually, at the top of a hill in the town, the bars came off. Lucky to be alive.
Back then (before I even registered with this forum - I was down and out, I didn't even have access to the internet) I was utterly clueless - I had no idea about torque, let alone torque wrenches!