First I bought a nice, light, reinforced roomy bag from Alchemy Goods. It is very surdy and lightweight and it is completely constructed with recycled materials. The bag is made of recycled banner material and the straps are used seat belts with the handle reinforced by used bicycle tires. The resulting bag is handsome, very strong and lightweight. Not inexpensive but I am very happy with it.
Now one bag will just not get me home from the grocery store. So I purchased a group of 5 nylon bags from EnviroSax They carry twice the amount of a typical plastic grocery bag and they are small and light enough to fit in a little sack in my glove compartment.
Now my major obstacle is just remembering to bring these into the stores! I have succeeded a few times so I'm hopeful I can be retrained. They are a pleasure to use - nice and strong and I'm not inundated with more plastic bags to litter our environment. So I heartily endorse both of these items.