I don't think I've contributed to a bicycle helmet discussion before, so here goes:
I wear a cycle helmet and I would not like to say if others should wear one or not, it's just my choice and it keeps my head warm.
However, I am also aware that brain injuries are caused by high g forces acting on the head. In other words, when the head, travelling at a nominal velocity, hits a stationary object (road, car, lamp post etc) it will come to rest very rapidly and thus the brain will experience very high g forces which will damage it.
In addition to a head, a motor cycle contains thick padding, many times thicker than a cycle helmet, so when the helmet strikes a stationary object, the helmet shell comes to rest very rapidly. But this time the padding inside the helmet will compress slowing the head down more gently, thus reducing the g force and also the likelihood of the brain being injured.
A bike helmet has very little or no padding inside it, so when the bike helmet strikes a stationary object, the shell again comes to rest very rapidly, but so will the head because there is nothing to compress. The head is virtually at one with the shell. This will result in a very similar g force to that experienced by the non helmet wearer. The likelihood of brain injury will be the same regardless of whether a helmet is being worn.
What a cycle helmet will do is to protect against superficial abrasions and cuts to the scalp, but that is all.
The cycle helmet industry will have you believe that their products cocoon you in some sort of safety shell. It's nonsense, Isaac Newton says so, they simply want some of the cash in your pocket.