Collect data on how many bags you bring home. Then help bring down this week's average by submitting your results.
Plastic bags use a lot of resources and energy to make and are hard to get rid of because they don't decompose. So, they end up littering the landscape and taking up a lot of room in landfills. Paper bags are not much better... they also need energy to produce, use up trees and water resources, and still end up filling up landfills. The best choice is to use fewer paper and plastic bags or not use them at all.
It's handy to get a bag from the store when you buy something, but do you really need a new bag every time?