Helmets protect your brain, period. They won't prevent a broken neck, but they don't help to cause them either. Odds are, if you fall in a way that your neck gets broken, then whether or not you were wearing a helmet will make no difference...it will only help to prevent a brain injury on top of a broken neck.
Now, don't get me wrong, I'm not one of those "ZOMG, everyone should wear a helmet always" types of people. I don't wear one, but I still recognize that they are a very cheap preventative and they do work. If you are still a minor, like BA said, then you should listen to your mom and wear one. If you are older...you can make your own decision but helmets are safer than going naked-headed.