Nero did not "fiddle" during the Great Fire of Rome (violins had not yet been invented, nor was he playing the lyre). In fact, upon hearing news of the fire, Nero rushed back to Rome to organize a relief effort, which he paid for from his own funds. He also opened his palaces to provide shelter for the homeless, and arranged for food supplies to be delivered in order to prevent starvation among the survivors. Finally, he made a new urban development plan that attempted to make it more difficult for fires to spread. However, it is true that he blamed the fire on Christians.
http://en.wikipedia.org/wiki/List_of_common_misconceptions
Edit: Here's another good one, humans have more than five senses. The truth is we're not entirely sure what is defined as a "sense" so the list ranges from 9 to 20 senses. Besides the well known 5 we have sense of balance, sense of heat, and proprioception (where a part of your body is in relation to the rest in space).