This Magnum Photos gallery will make you feel like stretching.
Stretch's effects may be similar, especially when linked to breathing. The very relief of muscular tension convinces your mind that it can safely relax. This may sound strange, because we usually imagine that the mind is in charge and that it tells the body what to do—"swing that baseball bat" and so on. But what we see here is the exact opposite. When you smile or tie yourself into a yoga pose, the body is, in effect, taking control of the brain. It is now the boss, telling the mind how to feel.
All this may make some sense, but I also like the "Jack London theory," which identifies most deep pleasures as an effort to fight the human condition and return to a more animalistic state. Consider that the main psychological differences between humans and animals reside in three places: the brain, the backbone, and the hands. We think a lot, stand on two legs, and use our thumbs to send text messages. Of course, these three body parts tend toward disaster: mental illness, back pain, and tendinitis. These three disorders, more than original sin, are the curses of human existence.
Stretch, then, is an effort to return to a more primitive state. You don't often see wolves with aching wrists or polar bears with sore backs. They were lucky to be spared our idiotic desire to stand upright or type. So when we manage to undo the tension caused by our stance, we are in some tiny way fighting millions of years of mistaken evolution; declaring war on the whole idea of Homo sapiens. Maybe that's why stretch feels so good.