In an article about the importance of form and function with regard to the face, one interesting point that was made was the fact the our noses (mostly our sinuses) make nitric oxide (NO), a gas that acts as a powerful vasodilator. When inhaled into the lungs, it promotes oxygen uptake. This is why we're told when running to inhale through your nose and exhale through your mouth. What this implies is that if you're a chronic mouth breather, you may be depriving yourself of oxygen.
Searching further on Pubmed revealed an interesting study: humming increased nasal production of NO 15 fold as compared with quite breathing. They hypothesized that oscillating nasal breathing as a result of humming could explain this process. It's also interesting to note that rapid short nasal breathing taught in yoga classes may have a similar effect.
I strongly recommend that you read the entire article (it's a little long). It's an interesting read about how poor development of our facial bones could be leading to many of our medical ailments today. I can't agree with everything stated in the article, but I do agree with most of the article and the basic fundamental arguments. It parallels and supports all the major concepts that I discuss in my forthcoming book, Sleep, Interrupted. It also references Dr. Weston Price's book, which I use as a one of the foundations for my book.