An obvious use for the jigsaw is to make your own jigsaw puzzle. Apply glue to the back of your desired picture, making sure you cover every part. Stick the picture on a board and clamp another board to it to ensure the picture stays flat and adheres well. Allow to dry. Draw the shapes of the interlocking pieces on the back of the board, following traditional jigsaw design. Cut them out carefully. Your jigsaw puzzle is now ready to put put back together.
Because a jigsaw can be used for fine and accurate cutting, you can use it to make things on a small scale, such as a dollhouse, complete with all the furniture. This is a project that can last you several years and give hours of satisfaction. For a really professional looking job, make sure you work to a consistent scale, such as 1:24. This means that 24 units (inches or centimeters) on the real furniture is scaled down to 1 unit on the doll's furniture.
Mass-market furniture tends to have fairly predictable designs because of the manufacturing processes involved. However, with a jigsaw, you can make furniture which allows your creativity to run riot. Why not have a desk top the same shape as a guitar? Why not make a cloud-shaped headboard for a bed? With a jigsaw, the sky is the limit.