Why it is impossible for a dropped penny to kill someone.
There are many variations of the story in which a penny is dropped from the top of a very tall building (such as the Empire State) and plummets to ground level, where it fatally strikes the head of a pedestrian below.
In fact, the falling penny would be far less harmful than most people imagine. Because the mass of a penny is around 3.5 grams (depending on the currency), the weight pulling it downwards is only 0.035N.
If dropped from a great height in a vacuum, the coin would accelerate downwards at 9.8m/s^2 until it hit the ground. By this point, if the height used was the Empire State (443m), it would be falling at over 300kph (83.3m/s). This would indeed be enough to kill an unprotected victim.
However, in reality, the friction of the coin against the air would force it to descend at a far lesser speed. Because the penny has (for its mass) a proportionally large flat surface area, it will experience a large aerodynamic drag force. Depending on wind conditions (and the type of coin used), the drag could result in a terminal velocity of only around 10m/s, which would be insufficient even to cause mild pain for more than a few seconds to anyone hit by it.
Sources: scientificamerican.com; howeverythingworks.org; science.howstuffworks.com