After reading this article on Etsy I decided to try my hand at fusing plastic bags. This process creates a thicker plastic that you can use as a fabric similar to vinyl or polyurethane. The article covers the process in greater detail, but basically you just iron several layers of bags together between sheets of paper.
After ironing the layers together, I trimmed the edges then decided to make a little pencil pouch out of the "fabric" I had created.
You can't tell from the picture because I shot it from its good angle, but the pouch is totally lopsided because I failed to make a pattern first or do any measuring first. It's ugly but functional! I only used half of the plastic so I might make something else later too. This took 6 plastic bags from my hoard under the kitchen sink. It's better than having them all end up in a landfill!