The benefits of exercise on the psyche are well documented, encompassing catharsis, endorphin release, mental health improvements and self esteem. There is also evidence that it increases cognitive function short and long term.
It would seem that these benefits are from more BDNF, blood with higher oxygen content, and more bloodflow to the brain. I would think the blood effects would cause the short term benefits, while aiding in the increased neurogenesis long term.
I just went for a run. I assumed the immediate(within the hour of exercise) clarity I felt to be attributable to the mood-altering affects(catharsis, stress relief, endorphins, etc). Quick searches show websites like ScientificAmerican and brainblogger et al confirm that more bloodflow to the brain contributes to state and structural changes in the brain.
However, in The Brain; A Very Short Introduction by Michael O'Shea, it mentions; [On the topic of areas of the brain requiring more glucose and oxygen] "A simple solution to this problem would be to pump more blood into the active region, much in the same way that a muscle is supplied with more blood when exercised vigorously. However unlike a muscle, which becomes engorged with blood and swells when exercised, the brain is confined by the skull and cannot be allowed to swell significantly. The solution to this tricky problem is to maintain a constant overall blood volume in the brain and to arrange for blood to be diverted preferentially to active regions.".
I'm skeptical of the bloodflow explanation, since there is the counter evidence from the book I cited. This raises a related question concerning blood though. "Would breathing air with higher oxygen content be beneficial to brain function?"(I'm aware too high and there isn't enough carbonic acid, no?).