I'm right handed and wear mine on my left shoulder/arm/hand. It's easier to get into as well being that I'm right handed. I can't wear it on my right at all, it feels too odd and it's difficult.
I'm right handed, but I prefer to carry my bag on my left shoulder. I feel like I can rummage in it easier with a right hand lol. Besides, for some strange reason, whenever I carry it on my right shoulder it tends to slip off and it's annoying.