I tie mine up because he tries to turn around and last time he did that he slipped and it took 3 people to get him up and out of the trailer, he wedged himself in. Mind you this was when we were trying to get him out, not while we were travelling.
I have also been told that it's safer to tie because if left untied they can get their head bent around the divider and become panicky, and that makes everything a whole lot harder to deal with. That's in a straight load though.
Mitch is tied loose enough to balance himself, but not loose enough so he can pull his ead around and get stuck.
R.I.P ~ Bubbles - 25yo tb mare - 13.04.2011 ~ 8:30am ~ passed away naturally and peacefully in my arms