I use only a backpack, since I've never had to buy groceries for more than myself. Sometimes I have a lot in my backpack, but I've never had any problems with back aches. I think the decent ones are pretty well designed to avoid strain on the back.
Actually, I feel naked when I don't have a backpack on. I tell car driving friends that it's my purse, my glove compartment, and even my car trunk.