Reusable grocery bags are a great way to reduce your environmental impact while saving money. According to this article from Treehugger.com, either paper or plastic bags are detrimental to the environment and to human life and health. The answer is to take reusable bags with you shopping. You probably do not have to go out and purchase bags to take. Before you purchase bags, go shopping in your closet. You may find canvas tote bags or beach bags that you have not been using that would be suitable to take shopping. Otherwise, thrift stores often have a variety of tote bags available.
Reusable grocery bags that have been offered by grocery stores over the past couple of years, although they cost a nominal amount of money (often a dollar or two), meet the criteria for saving money because many grocery stores will give a 5¢ or 10¢ credit every time the bag is used. Therefore, the bags will pay for themselves in as little as ten uses. Since these bags are designed to be used hundreds of times, the savings will gradually add up. If you are purchasing bags, look for ones that are designed for 500 uses per lifetime.
If you don't want to purchase reusable shopping bags, you can reuse the paper and plastic bags from the grocery store. You will still be saving resources by giving these bags an extended life. Grocery stores typically will still give you the bag credit for reusing these bags. If you chose this option, I suggest using paper bags and ask the bagger to make them full. Paper bags are designed to hold much more then plastic bags and you can usually get many more uses out of them. When the bag rips, recycle it.