|I saw this question on the message boards, but my computer wouldn't let me reply to it [for Melissa in NY].
I have covered boxes with regular fabric, using spray-on glue. You'll want to do this outside because of the fumes. Spray each section of the box [not the fabric], and smooth the fabric over it, then go on to the next section. A thin but tightly woven fabric works best, so that your lid will still fit onto the bottom of the box.
If you want to protect the fabric, after the glue is completely dry, you could spray it with Scotchgard®. This won't add any extra thickness, so again, the lid will still fit. Personally, I just vacuum my fabric covered boxes with the brush attachment.
This is an amazingly fast and easy project since spray-on glue was invented.
Another tip...be sure to read the directions on the glue can. Mine says to hold the can upsidedown when you're done, spraying for a few seconds to clear the nozzle, just like spray paint.
Have fun...and beware, lol, this is addictive. You can get as creative as you want, adding ribbons, fabric paint, appliqués, a fabric handle on top, etc.