Over here we're rather environmental (need to as we have hardly any resources). Free plastic bags are an endangered species nowadays. Usually, plastic bags cost 15-60 cents a piece, depending on size and store. Sadly, paper bags are rare; they cost 15 to 30 cents but are much bigger and sturdier than the plastic ones. Most shops have cotton bags that cost 75 ct - $1.25 Their quality differs widely from veil-thin to suitable for carrying an elephant.
People who come by car often bring foldable plastic boxes that fit in the trunk.
Btw, here you are supposed to pack your stuff yourself. And quickly, because the rest of the queue is impatient and the lady at the cashier mercilessly shoves the next customer's stuff over the scanner into your heap.