What is very clear from everyone's comments on this blog, is that to some extent mind does influence matter & our health. The question therefore is: How much? and is there somehow an undiscovered or undeveloped potential here? Awareness exercises will show you that you & everyone else live in a very small fraction of what goes on in your head. So if we could quiet all the monkey-mind, the rather insane thoughts & disorganized energies which lie below our convincingly hypnotic, though inaccurate sense of self; if we could bring all that energy of our consciousness fully into the moment, isn't it possible, or doesn't it even seem likely, that this new Mind, so foreign to us in the West, could have a much greater effect on our bodies & perhaps even our surroundings? The place to explore these issues is in our own minds, not out in the external world. Consciousness is like a light, a flashlight in the dark. The more of it you bring into the present moment, the more you can see. But like the Buddha said: don't take my word for it, find out for yourself, if you care to.
Roland is right, there is no "untapped" part of the brain/mind that would make us so much more powerful if we could somehow use it. The unconscious mind is there to handle both basic tasks and second nature tasks. Two examples would be breathing and athletics. You don't need to think about breathing, you just do it so your mind can focus on other things. In professional sports, an individual typically has to focus on what they are doing as they learn it. As they become more skilled, however, they don't have to think about what they do. Their general motions are controlled by their unconscious and trying to think about it in this situation usually leads to decreased performance. This allows us humans to learn and solve problems physically and mentally. This is why the unconscious exists, it is not some hidden potential for us to unlock. It is explained in detail in David Eagleman's book, Incognito.
Now, introspection, meditation, metacognition, etc. are practices that certainly don't hurt and people can benefit from them, they are just often hyped up to be more than what they are. Your mental states also can influence your health but the mechanisms for that are known and they do not involve a force of mind over matter.