I'll start with a common one, that yes, I've done too. Failing to put the chain on the big chainring before removing the DS pedal. When it cracks loose, you get tooth marks.
And speaking of freewheels, I've tried to remove a cog from one that I didn't know had reverse threading and blew apart a chain-whip.
And since I seem to be on chains, I forget exactly what I was doing, but it involved a fixed gear drivetrain, and resulted with a finger jammed between the chain and the chainring. No derailleur give. Ouch.