Let's just get this out of the way up top: No, a penny dropped from the Empire State Building cannot kill a pedestrian below. But the interesting question is why not?
The answer starts with terminal velocity. If we calculate the maximum speed a penny can achieve due to acceleration from gravity minus drag from wind on the 1,250-foot drop from the Empire State Building, we get a speed of perhaps 30-50 mph, depending on various assumptions made about wind, the orientation of the penny, and so on. In the clip below, the MythBusters start by shooting a penny at about 65 mph to test the highest conceivable speed a penny might achieve.
Where it gets interesting is sorting out just how much this would hurt. If somehow you were hit by a falling penny, would it break the skin? The MythBusters try this, and predictably scale up the test to the point where they're effectively shooting a penny like a bullet. At one point, Adam Savage takes a penny for the team...and lives.