The Left. I just have to walk in from the Left. Even if I entered from a turnstile all the way on the right I'll walk across the Mickey flowers and enter through the left. I have no idea why. I've entered through the right only when it was extremely crowded (and I felt lopsided walking in that way). I don't have any other quirks (that are Disneyland related).
We go to the right -- no idea why. Always have. We exit on the other side which would be the left upon entering, so I guess that means that we exit to our right also, but it's the left side. Ouch, my head.
The right side. I don't know why but I tent to head that way after the turnstile. I sometimes got left but very rarely. I don't really have a reason beyond when I was younger my family always went right.
Both directions facing the Castle:
1. Right side in (entrance lines are usually shorter on the right, due to the herding mentality of those getting off the M&F shuttle);
2. Left side out (closer to the shuttle).
"Here You Leave the World of California Today and Enter the World of, um, er, California Today."
Right side on EE days, left on non-EE days. On the non-EE days it just feels shorter going to the left to get my Splash FPs. On EE days it seems quicker getting to FL. Why? I have no idea but I've been doing for quite a while.