This is probably the most widely asked question (after people become aware of the controversy), and one of the most difficult to answer.
It depends very much on what you mean by work, I guess. According to the standards, helmets should be able to absorb most of the energy of an impact on a flat surface from a stationary or slow-moving bike. If you fall off, the helmet should, in theory, absorb most of the energy.
As far as I am aware, they do that reasonably well, although the standards have undoubtedly become much weaker over time and few helmets now on sale meet the best standards, those of the Snell Memorial Foundation. Although it’s quite common for helmets to fail on test, and in the USA most are tested to a self-certified standard not one administered by an independent body, overall I believe there is fair evidence that they do as the manufacturers claim.
New Zealand data shows no correlation between helmet wearing rates and head injury rates
You will note that none of the manufacturers claim that helmets will prevent serious injury. Or that they will protect in collisions involving motor traffic. In fact, they often say they won’t protect in those circumstances – which is fair enough. As has been pointed out by other, more combative writers, bicycle helmets are made of the same stuff you discard when you buy a new television, and you would laugh in the face of anyone who told you that a TV or computer in its box – often with far thicker foam – would be expected to survive an impact form a moving motor vehicle. The very idea is patently absurd.
This, then, is the core of the problem: those promoting helmets raise a false picture of the kinds of injury they can prevent. Sometimes this results in helmet laws. The gulf between the claimed (or insinuated) capabilities of helmets, and their real capabilities, is at the heart of why helmet laws fail.
So, helmets work as claimed by the manufacturers, and as tested, but this is a long way short of working as claimed by their more aggressive proponents.
The fact that they are promoted almost exclusively as a road safety measure – road traffic law is easier to pass, I guess, than laws restricting what we do in our own time on private property – is problematic. As a road safety device they are a non-starter, since they are absolutely not designed or tested for the dominant source of serious injury on roads. In that context, they definitely do not work. At least, not as they are pretended to.