The answer is foldable shopping bags. Any intelligent person that regularly go to stores during lunch breaks or when commuting is either always carrying a backpack or a small foldable shopping bag. There are many folding bag designs that fit into your pants backpocket.

I have no car and I very rarely leave home with either a foldable bag, a backpack, a drawstring bag and when I don't have one of those that is usually because I am using my bicycle which is equipped with a basket and panniers on the rear rack, or my motorbike with its top case.