A natural adjunct to crafting hobbies is photography. Get a quality camera and teach yourself and your child to take good pictures. Learn how to light crafts projects best and commit them to film. Explore different ways these photographs can be used, including manipulating them in your computer.
Another way to show off crafts, depending on the size, is in one of those coffee tables with a glass-topped display case built in. Change the display monthly and share new craft projects with everyone who visits. This type of display-case coffee table would make a good furniture-making project for an adult.
If your child's favorite craft usually takes the form of something flat, make a place to hang things on the wall and rotate with new versions as they come along. A large clip-and-glass frame (the kind made of two pieces of glass pressed together and held by clips) can accommodate different-sized pieces.
Or how about a large bulletin board or a bulletin board border? Using 12-inch cork squares applied directly to the wall with an appropriate adhesive, create a border at about eye level around an entire room or along one wall. This would work well for a play or rec room. You can even band the cork border top and bottom with wallpaper trim. Now you have plenty of space to exhibit your child's latest works of art or anything else you'd like to show off.
Paper cutouts look beautiful on a window. Share them with the whole neighborhood. When my kids were little, they made some pictures, set up a table at the end of the driveway and made a big sign that said "Art Show." A few neighbors even stopped to look and one offered to buy a couple.
Why not have a neighborhood Arts and Crafts Show and Exchange? It could be held in someone's yard or garage and kids and adults could show what they do. We used to have a similar event where I worked. It was a Family Day and employees and their families brought in their hobbies to show. Consider this for your church or community organization.
Ask the staff at a local nursing home or hospital if they might like to borrow some colorful crafts to display at their facility. They may even want your child to come in and explain how the project was done. Combine bringing the crafts to display with a visit with some residents. Bake some cookies for the occasion.
Perhaps your child wants to preserve the memory of a project, but you don't have room to keep the project itself forever. Consider making a scrapbook. Take a picture of the project and incorporate it into a scrapbook, which becomes another craft project in itself. This can become a kind of portfolio and record you child's progress and changing interests.
If a lack of space is a consideration, how about scanning the picture (or having it scanned) into your computer and keeping picture files of projects? Take it a step further and put up a family Web site where you and your child can share crafting experiences and results with other families.