Strange anecdote: I once organized a workshop on reasoning about uncertainty and one of the attendants was a health official working on bike accident statistics. According to her, if going solely by the statistics, helmets would have to be prohibited in our country because people riding bikes with helmets had a significantly elevated risk of grave traffic accidents in comparison to those without helmets. Of course, she also said that you really couldn't use the statistics in this way and we agreed that it seemed likely that helmets could prevent serious head injuries.

Still, it was an odd finding. Presumably, people with helmets drove faster or more carelessly but she did not have any evidence for that at the time.

Edit (just in case): 1. I'm not an expert on any of this and it's just an anecdote. 2. I recommend wearing a good, certified helmet.