You can have elegant fabric wrapped gifts in the Japanese style with the linked directions. This is the art of furoshiki. You can try this with any fabric, but if you use a scarf or other useful item it becomes part of the gift. This probably won’t work well with all sizes of gifts, but it’s worth a try. They do show how to wrap different shapes of items that are quite inventive. There is even a way to wrap a wine bottle that makes a nice presentation. Click on the label “wine bags” below this post for ideas on making wine bags from fabric. I think most peole keep those to reuse.
Japan is encouraging its people to not use disposible gift wrap, like paper, bows, and tape. In the US we are starting to give gifts in reusable gift bags, but this is another step to consider. To make sure the fabric is not thrown out after opening you might want to include a note about its purpose.
Click title for link to the Japanese picture tutorial I found via FaveCrafts. I’m printing it out to keep with my gift wrap supplies.