“I went to the store. I bought a wastebasket. The cashier put it in a bag. I brought it home. I took it out of the bag. I crumpled up the bag and tossed it in the wastebasket.” ~ Lily Tomlin

For small purchases do without a bag
This alone could save hundreds of millions of bags

Stop using plastic bags
They are made from petroleum products and tend to end up in the dumpster or blocking drains, choking wildlife. They are not biodegradable, even if they say they are they do not decompose fully. Also the ink is made up of cadmium, and is highly toxic when it is released.

Bring a cloth sack or string bag when you shop
Paper bags are reusable and biodegradable, however many supermarkets use paper that has never been recycled before and they always say "recyclable" not "recycled".