Paper, or plastic? When people in America buy groceries, they tend to buy about a week's worth at a time, and this is more than can readily be carried by hand. So markets typically provide bags for easy carrying. Almost all of these are immediately thrown away once the groceries are safely in the refrigerator or pantry. Those that are kept are reused once, again to hold something.
This wouldn't be a problem, except that stores go through thousands of bags per hour, and the plastic bags will remain in their current form for geological periods of time. Should they blow loose, they clutter up (and ugly up) the nearby environment, and harm turtles when they blow into the ocean, and the turtle confuses them with a tasty jellyfish.
The bag can be recycled, by melting it down and running it through an extruder to give it a new shape. But Discovery news reports that a laboratory in Illinois can turn them into fuel. For not much more energy than recycling them would take.
The lab heats them in an airless environment, until the atoms dissociate from each other. The hydrogen is siphoned off for the many uses of loose hydrogen, and the carbon forms into "microspheres," (which sound a lot like buckyballs), which have a thousand-and-one uses. The lab hopes that this will change the economics of plastic bags, such that hobos will cheerfully gather waste bags for money. Quickly, the landfills would empty, and no more would a turtle choke to death on something that existed only for hauling a bunch of food for a few hours at most.