This entry is a Bike Hacks classic. Trevor sent us the following way back in 2008.
I just developed a bike hack that you might like. I call it "The $4 Grocery Panniers". I wrote a how-to over at bikeforums.net. (see the forum for full instructions and more pictures).
All you need is:
* 2 reusable grocery bags
* 1/4" thick 2'x4' piece of masonite (or "hardboard" at Home Depot; same stuff used for clipboards)
* 1 bungee cord