Usually when I'm with my guy friends and we're out at night, or even during the day and walking around, they never let me walk on the cars, they always stand on either side of me, so I'm in the middle. But, when I'm with only one of them, they usually stand on the car side, never really heard of the mugger theory..
i've never even considered such an idea before. but as a personal preference I prefer people on my left, guys or girls, because I find for some odd reason it's easier for me to turn to them and pay attention when they're talking... I actually will move to their right if I found myself somehow at their left. often they'll just stop and be like.. what are you doing ;p
Neither... I usually walk on the opposite side of her purse, especially if it's a bulkier one. If you walk on the same side as the purse then I feel distant or it prevents hand holding, etc. Although, if we're in the city, I make a point to stand on the inside of turns (IE: on the left if you are turning left on a block) when they are blind turns (blocked by corner of buildings). This is because drug dealers and homeless usually linger near the corners up against the buildings and will target women first. This has been my experience in Saint Louis city, at least. I had never heard of the "mugger theory" either, but began doing this after a homeless person grabbed my ex's arm.
But unless I'm in the city past 11pm, I don't really worry about which side I'm on :)
Walk on the right side to keep her away from on coming cars, and same goes with puddles if you have to walk through a puddle the guy is the one who takes the hit from it, because well we are men and a little bit of water on our shoes isn't going to kill us, now if a chick has to do that she might think it is worse than death to get her shoes wet.