Don't put your hands near the belt of a running automobile.
Don't put the car in gear without somebody to hold the brake pedal unless you have the wheels up in the air (the front wheels for front wheel drive cars, and the rear wheels for rear wheel drive cars).
Don't work on a car without taking the positive battery cable off the battery first. This can help prevent shocks.
Do not attempt to fix your car during or immediately after a car accident.
Don't stand in line with the fan that cools your radiator when your car is running. Fans have been known to break (especially when you accidentally drop tools into them) and you don't want to be in the path of any potential shrapnel.
Tie back long hair when working on your car. If the car is running you could get it pulled out.
Never take the radiator cap off your car while the engine is hot. This system is pressurized and the water will come out at high force if it is hot.
Don't work on a warm car unless you must. It is easy to get burns, especially from the exhaust manifolds.
Never work under a car held up by a jack. Put jack stands under your car to prevent getting pinched.