We have been using fabric scraps as gift wrap for a number of years. There is no reason to waste paper. The fabric is totally reuseable and something we already have.
We have found it a bit tricky to wrap some packages. We have resorted to safety pins and ribbons. To make it simpler, CRAFT:magazine has a link to a PDF on a website from “The Ministry of the Environment Government of Japan” which details several wrapping methods.
Click the image and download the PDF. Awesome!