Just another unoriginal take on the question, "Paper or plastic?"
You can reuse (and thus, reduce) plastic bags by turning them into a "yarn" and knitting the bags into a grocery bag. Here is a pretty clear tutorial, and the result isn't half bad.
For the more advanced tree-hugger, it is possible to spin newspaper into a durable "yarn" as well. I don't spin yet, but think this is a pretty neat idea.