Mouth breathing has a poor reputation in our society. A 'mouth breather' is someone of low intelligence or poor social standing, someone so uncouth and uncultured that they never leaned to breathe through their nose!
There is, however, a good medical reason for the nose-breathers to look down on the mouth-breathers. Humans are 'obligate nasal breathers', in that breathing through our nose is important to developing normally and staying healthy. Chronic mouth breathing, especially in infants and young children, can be a serious medical problem, and should be brought to the attention of your doctor.
First off, as we all learn in school, the sinuses of the nose function to warm and filter the air on its way down to the lungs. The sinuses also produce nitric oxide, which has an antibacterial effect. Thus, mouth breathing slightly increases the chances of sickness, lung infection, asthma, and dehydration.
During mouth breathing the tongue, which normally rests against the roof of the mouth, drops to the floor of the mouth to allow air to pass into the back of the throat. The jaw, which usually rests with the teeth lightly pressed together, opens slightly. As you can see, the default nose-breathing resting positions are not actually truly at rest; the tongue pressing lightly against the roof of the mouth and the jaw holding the teeth together requires a slight but constant bit of muscle control. This exercises these muscles and helps develop good muscle tone; in the absence of healthy resting postures, the proper muscle tone does not develop. Oral hypotonia can have adverse effects on speech, feeding, and swallowing.
Not only does the resting posture of the jaw aid in building muscle tone, it also effects the timely eruption of teeth and guides good occlusion of the teeth. The constant light bite of a healthy jaw keeps the jaw in alignment, preventing the formation of an overbite. If even a slight malocclusion forms, this can result in undue wear and tear on the teeth and accelerated dental decay. This may result in other issues in the long term, such as TMJ problems.
It also appears that nose breathing increases the air pressure in your lungs. Because the nostrils are narrower than the mouth, air cannot escape as quickly when you exhale through your nose. This increase of pressure helps to maintain the elasticity of your lungs, and appears to prevent diseases such as atelectasis (alveolar collapse).
During sleep, mouth breathing predisposes you to snoring and irregular breathing, which in some cases may cause sleep apnea. Sleep apnea has been linked to long-term increases in mortality rate and is suspected to play a role in SIDS.
And on top of this, good oral health requires our teeth and gums to be constantly washed in saliva. Mouth breathing causes this saliva to dry out or pool behind the front lip (or in some cases, fall as drool). This can cause gum irritation and bacteria growth, which in turn can result in a host of oral diseases.
It is often claimed that mouth breathing also causes craniofacial deformities. This is somewhat uncertain, and some studies have found no relationship between the two. It is possible that pressure from the tongue helps flatten and widen the plates of the hard palate, and may help in the correct formation of the alveolar ridge. The dropped jaw results in the appearance of a long face, and nasal blockage may cause a widening of the bridge of the nose. And as stated above, it may cause an over- or underbite. Other than these factors, I have been unable to find any real evidence of craniofacial growth problems.
Nasal obstructions are particularly dangerous in infants, as infants cannot suckle and breathe through their mouth at the same time. Given a choice between breathing and eating, they will choose breathing (good choice!), and may suffer from weight loss and malnutrition. It is worth noting that weight loss is always a bad sign in infants, as they should be growing rapidly, and thus constantly increasing in weight. They also should keep a healthy layer of baby fat, which will provide energy reserve during sickness; this layer of fat is a safety net to help the infant through temporary sickness during which they cannot feed properly.
Although not necessarily caused by mouth breathing, many problems co-occur with mouth breathing. Nasal obstruction may result in middle ear infections, head, neck, and face pain, and sleep disturbances. Nasal obstructions may also be the result of serious problems such as sinusitis, adenoiditis, a deviated septum, broken nose, nasal polyps, or severe allergies, many of which have serious symptoms other than mouth breathing.
But don't panic just yet! Mouth breathing is to be expected during exercise, while speaking, and when taking particularly deep breaths. Yawning and sighing are perfectly fine mouth-breathing activities. Colds and allergies also tend to result in temporary periods of mouth breathing, and that's okay. You should be concerned only if a child routinely breathes through their mouth, and particularly if they seem chronically unable to breathe through their nose.