As a practitioner of kung fu, it truly saddens me that the importance of the breath is neglected during most discussions of martial arts that I encounter. Deep breathing as mentioned here is the first breathing exercise we are taught at my dojo.
Even if one is not a practitioner of the martial arts, learning to breathe naturally from the hara can be beneficial in many ways. To foster the proper development of deep breathing our sifu recommends this practice once a day:
First off, lie on your back. Place one hand on the chest and the other hand on the stomach. As you breathe, make a conscious effort to raise the stomach hand with the inhalation and let it fall during the exhalation. The chest hand should remain stationary.
The goal is to develop this breathing pattern until it happens subconsciously. I find that when I practice this exercise right before bed it relaxes me so much I have no difficulties in falling asleep.