If you'll have a look at the pictures below, you'll see that people have some very creative ideas for what to do with old puzzles. Magnets, pins, and even completely altered puzzles have been the top crafts that I've seen, as well as some other kichey kids crafts.
Depending on what you want to make, you find a few puzzle pieces with a naturally pleasing design, or you can paint it or use newspaper, gift wrap, or scrapbooking paper to cover the puzzle pieces. If you cover with paper, you must file the edges with an emery board to tidy it up.
Next, you let your imagination run wild and add embellishments which seem to range from a variety of notions, hardware supplies, and even hand drawn art. Finally, you attach a pin at the back, or a magnet. Totally amazing! What a really neat homemade gift.
I'm going to give it my best shot because at the very least I'll have fun doing it. I may have to pick up a better, faster drying glue though. If you never hear another word about it, it's because they turned out really hokey and I don't want to embarrass myself by posting pictures of crafts that look like a grade school student made.