Cardboard is the ultimate material for creating family-style fun stuff out of recycled materials. It's cheap and therefore plentiful, and if it's in good shape, it's sturdy enough to build structures with. For easy rainy day fun, have your kids create picture frames out of cardboard. You cut the shapes and then let them decorate them as they see fit. You can even create a stand for the back out of another strip of cardboard.
On a larger scale, kids' playhouses are great uses for cardboard on its way to the recycle bin. Simply set up the boxes, cut a few windows and let the fun begin. Kids can spend hours playing make believe in their very own home for the day. And if you ever find yourself the beneficiary of an unexpected snowfall, a piece of cardboard will serve as a ready makeshift sled in a pinch.