I was going to wait to post this until the challenge involved unusual materials, but I've had a couple requests to post the information now.
One of the ultimate recycling projects, is utilizing things like potato chip bags, magazine pages, or candy wrappers to construct a purse.
There are several techniques to do this, even as simple as
basic decoupage.
Or the next step would be a simple weaving technique.
Most of you have probably seen simple ribbon weaving in projects, so just take this idea but use paper.
This technique may have originated from Mexican paper weaving, or from Polynesian weaving of palm fronds, etc.
Some fun examples:

A purse made from woven magazine strips, for sale at
Wonders of the World.

Awesome tote woven from newspaper by
Uncommon Goods (this site so totally rocks).
Newspaper and Duct tape bag on craftster.
Small wallets woven from junk mail, available for purchase at
Junk Mail Gems.
Same technique
here, but Carol Duvall made placemats and napkin rings, using wrapping paper.
But take this all one step further, with folding and more intricate weaving, and you've moved into the realm of folk art.

Silver Utra bag by
Ecoist, made from woven candy wrappers.
Hard to believe, huh?
Ecoist constructs these by hand, using recycled materials used to make candy wrappers, food packages, and soft drink labels--stuff that would normally wind up in a landfill.
With each bag sold, they plant a tree.

Checkered baguette from
Sweetie Purse.
This technique of weaving cigarette packs or candy wrappers into objects is referred to as
Tramp Art, or sometimes Prison Art.

Purse woven from Kools cigarette packs, by Leland Dodd.
More info
here.
(click photo to enlarge. Note the tramp art link above carries this same image, along with another from a different booklet)
This how-to is from a vintage booklet called
Gum Wrapper Sculpture.Or the same info is
here.
Or, if you prefer an online tutorial, here's one from
Cut out and Keep, for making a candy wrapper bracelet.
It's interesting to note that the word 'trash' in Spanish is basura.
Basura Bags makes bags woven from chip bags off the streets of Honduras.

More info
here.
The organization Grupedsac is helping poor Mexican families become self sufficient through selling purses woven from candy wrappers, potato chip bags, and cookie packages.

More info
here.Similar product by
Georger Vargas.
Candy wrapper purses also available at
It's our Earth,
Global Folks,
Nahui Ollin, and a multitude of other places, including any of stores within the Museums of Modern Art.