Take your own canvas bags, shopping basket, or reused plastic bags with you when you shop. If you have a choice between paper and plastic bags, choose paper, which is more easily recycled than plastic, though it consumes almost as many resources to manufacture. Of course, first reuse it if you can, perhaps to wrap parcels for mailing.
Want to help convince manufacturers to use less packaging? Send packaging back to manufacturers with a letter telling them that you won't be buying their products again because of the excess packaging. Stores and manufacturers will get the message if sales drop for heavily packaged items or products in nonrecyclable packaging.