This BBC News article discusses new research that correlates different personality types with the position people sleep in. For instance, the most common position (41%) - the foetus position - allegedly are initially shy and have externally tough but internally sensitive personalities.
This is yet another of the long string of studies of the dispositional paradigm which purport to relate almost anything you can think of with personality "types". I am increasingly skeptical about such research for various reasons, but mainly because I think personality is a much more complicated affair than assigning pseudo-permanant features to people. I can almost bet that either you didn't fit into any of the sleep positions or you fit into several categories or always sleep in different positions. Further, even if your sleep position was constant and in one of the categories, the description of the category either didn't or rarely fit you or was too general so that it could fit almost anybody.
Nevertheless, this link -is- an amusing read.