I made one of these for my Biology class. It doesn't take very long and it looks pretty cool in the end. The one I made for school is colored. I've also made another one without using tools. Any way, here's what you need:
1 sheet of 8.5" by 11" paper
This can actually be done with any size of paper. This works best when the width of the sheet is around 8- 9 inches.
This could be used as a fun, cheap way to teach about DNA. Students would learn about the structure of a DNA strand and about how the four chemicals (Guanine, Adenine, Thymine, and Cytosine) combine in long complex structures to create the blueprints for what the cell makes.
NOTE: The DNA in the photos twists towards the left. As explained to me DNA actually spirals to the right. This is just a matter of which way you make your folds. Thanks to yardleydobon for pointing this out.