Hmm, my sleep patterns are positively mundane compared to the anecdotes shared here.
I will say I am far more prone to snoring (or possibly just snoring far more loudly) if I'm flat on my back and will startle myself awake if I'm just drifting off and make a loud "snort". Also, I tend to dream more vividly, or maybe I just recall them with better clarity if I've been sleeping upon my back. And since the events I recall tend to be unsettling, I try to avoid sleeping on my back. My preferred position is quasi-fetal, my left side against the mattress.
(On a semi-related note, I've read if one has a "dominant" side to his or her body, the other side tend to be a bit more limber. That's seems to be the case with me. I can bend my left arm and leg into tighter, somewhat more "odd" positions than my right limbs. As such it seems as though the left side of my body and handle the weight a bit better, thus motivating me to sleep with that side against the mattress.)