Chapter 7 ("What to Do with Your Mind") of Mindfulness in Plain English by Bhante Henepola Gunaratana muses on some phenomena that often come along with "following the breath" as a tool for calming and observing one's mind:
... Do not be discouraged if you find your own will getting in the way. Just use that as an opportunity to observe the nature of conscious intention. Watch the delicate interrelation between the breath, the impulse to control the breath, and the impulse to cease controlling the breath. You may find it frustrating for a while, but it is highly profitable as a learning experience, and it is a passing phase. Eventually, the breathing process will move along under its own steam, and you will feel no impulse to manipulate it. At this point you will have learned a major lesson about your own compulsive need to control the universe.
Breathing, which seems so mundane and uninteresting at first glance, is actually an enormously complex and fascinating procedure. It is full of delicate variations, if you look. There is inhalation and exhalation, long breath and short breath, deep breath, shallow breath, smooth breath, and ragged breath. These categories combine with one another in subtle and intricate ways. Observe the breath closely. Really study it. You find enormous variations and a constant cycle of repeated patterns. It is like a symphony. Don't observe just the bare outline of the breath. There is more to see here than just an in-breath and an out-breath. Every breath has a beginning, middle, and end. Every inhalation goes through a process of birth, growth, and death, and every exhalation does the same. The depth and speed of your breathing changes according to your emotional state, the thought that flows through your mind, and the sounds you hear. Study these phenomena. You will find them fascinating. ...
... the music of the moment — not to be intellectualized or analyzed or controlled ... but to be experienced and embraced and lived within — simply the Now.