There are really
23 questions:
1) Do helmets reduce the risk of serious head injury/death when accidents happen?
2) Do helmets increase the risk of accidents?
3) Do helmet laws increase the risk of other negative health outcomes?
I am going to leave #2 and 3 alone for now, because I really don't think that there is very good data to support either side. There are various mathematical models based on various assumptions, but I haven't seen anything at all convincing based on real world data. I'm sure everyone knows how spurious it is to compare Denmark/Amsterdam with their bicycle infrastructure and lack of helmet use to the US/Australia with their higher helmet use and relatively crappy bicycle infrastructure.
The answer to 1, as much as people cite "well, there's a study that showed..." is almost unequivically YES, they do reduce the risk of head/brain injury DRAMATICALLY - 75-88%, whether or not cars are involved in the bike accident.
The gold standard for meta-analysis/review of available evidence is the Cochrane Collaborative, which requires reviewers to use systematic methods to gather, review, and assemble the best available research-based evidence from published peer-reviewed literature which meet established criteria. They most recently published on this issue in 2009.
http://www.thecochranelibrary.com/userfiles/ccoch/file/Safety_on_the_road/CD001855.pdf. combining the data from the studies that were included into a meta-analysis, they show a dramatic reduction in injuries to the head, upper face and midface, but no difference in injuries to the lower face (which also acts as a control for the data as teh helmet doesn't cover the lower face). They don't explore the effects on mortality. I'm not sure why, but my guess would be that mortality rates are much lower than brain injury rates, meaning you need much larger samples to get meaningful data.
If you want to rehash the head/brain injury rate with/without helmets, I'd urge you to follow the link, scroll to the discussion, and read the feedback section where the authors respond to the various criticisms of
helmet law the research showing risk reduction in helmeted vs non-helmeted accidents. If you read the whole Feedback section, it also provides a very good background on study design, ecological studies vs case control vs time-series, and the merits and shortcomings associated with those study designs. Sort of a mini-epidemiology course.