The enWikipedia article summarizes the best/only real research on positions that I am aware of. I read a book in high school (that is to say it was old and I have no idea what the title was) that claimed that the semi-fetal position was the best, as it supposedly maximized protection without compromising breathing too much. I can't say I've seen anything that would indicate your head's direction actually matters, except as it depends on the position of the rest of your body. Do you mean facing North or the door? That's some Feng Shui stuff or something similar, which is meaningless.
In terms of which side to sleep on, there is actually an answer! Well, maybe. Sleeping on your left side aggravates heartburn more than sleeping on the right side1, but sleeping on your left may be somewhat associated with heart problems.2 From what I can read from the studies, the heartburn one sounds more causative, but then again dying is worse than a little heartburn... In the end, though, about the only thing that matters is that sleeping on yours side can lower the amount of snoring (annoying) and sleep apnea (unhealthy).