A helmet might not guarantee safety, but it is an effective protection against a brain injury. If you fall off your bike and break your collarbone or leg or something, it's not really a big deal. Bones heal with virtually no permanent damage, brain injuries don't.
It isn't about removing all risk - some danger is inherent in pretty much everything you do. The point is to manage the risk, and take acceptable precautions where they are convenient.
Anecdatum: I recently learned that an old friend of mine had died in a bike accident. No other vehicle was involved; he hit a road hazard (I'm not sure exactly what, but perhaps an uncovered storm drain) and landed on his head. He was wearing a helmet, but it didn't save him.
I've always worn a helmet when cycling -- and I'll continue to do so -- but I've never had an accident in which it mattered, and I don't think it changes the odds as much as you suggest.
As i said, a helmet doesn't remove all risk. I don't mean to imply that as long as you're wearing a helmet you're invincible.
There seems to be a strong opinion in these comments that because a bike helmet isn't a magical force field that prevents any possible injury, you shouldn't wear one (with the implication that because helmets don't protect you from every possible injury, you shouldn't ride a bike). All i'm trying to say is that helmets are better than no helmets, and no matter what safety precautions you take, risk is inherent in everything we do.
Helmets better than no helmets is not necessarily true, strangely. Perhaps on an individual right-now level, but not long term. The reason: the biggest protection you can have as a cyclist is lots of cyclists on the road. Helmets lower bike use, so in the end you'll be a lone, vulnerable road warrior...
Btw, would you also wear your cycling helmet while walking on the pavement as a pedestrian? At least in the Netherlands there are more head injuries for pedestrians that fall or hit something than cycling-related head injuries. :-)
It isn't about removing all risk - some danger is inherent in pretty much everything you do. The point is to manage the risk, and take acceptable precautions where they are convenient.