I came across this little post recently about WHY we lie on the right side after savasana. Everyone in yoga wonders it eventually because it's consistent across pretty much all classes. It's a great discussion to have, and a nice concise post about the topic.
The articles lists three reasons, and I'm going to make you go there to find out what they are because I try to avoid all out plagiarizing of content. Personally I've always heard we did it because it balances out the masculine and feminine energies. I've always been content with that answer even if there's not exactly a lot of scientific evidence to back it up. I'm going to just stick with that because the other reasons given, to me, just sound like a bunch of trumped up hokum. Maybe all three reasons will resonate with you... or maybe you think the whole thing is BS.
Read the whole thing for yourself at International Orange.