I actually brought my chihuahua to the dollar store a couple of times (I use to work there, so it was ok with the owner) and to the Coach store. I called Coach before I went in to see if it was ok to bring him in since I was looking at collars and I wanted to see if it would fit. They were totally ok with it and encouraged me to come back anytime.
IMO, my dogs are like my children. I would not leave a baby in a car....and I would never leave my dog in the car. However, if I know he can't go inside the store, he definitely stays at home with someone.
As for big dogs....yes, I feel they get a bad reputation and would probably love going inside stores other than Petsmart/Petco. I would love to take my sister's pitbull inside Coach, lol.