To store my origami paper (specifically the 15cm x 15cm sheets) I have been using a box that once held a desk calendar. It was flimsy, falling apart, and all around bad. So I decided to construct a new box that would house my nice paper.
This new box is made from scrap wood in the basement. I carved the pieces so that the walls came together as finger joints that were held by friction alone. Then I cut grooves along the top and bottom of each wall so that they would hold two flat boards, one for the floor and one for the lid. At this point, I also lowered one wall so that the lid could slide out of the box.
I sanded it all again and then used a wood burner to draw the image of an orizuru on the lid, just in case people didn't know what the box was for! And finally, to protect the wood, I put two layers of varnish.
I am very proud of my box. It's not perfect, partly because the wood was scrap, and partly because I am an amateur, but it will serve well for a long time. And, I can proudly say that there is not any glue or metal in the final construction.