If composting leftovers in the backyard or in a countertop composting machine, consider using shredded paper in addition to food. Red worms enjoy eating through shredded paper and will quickly eat and digest it, turning it into nutrient-rich fertilizer for your home garden or landscaping needs. If composting in a more traditional manner of digging a ditch and filling it with compost material, shredded paper will decompose faster than paper than is left whole.
Using shredded paper to fill water bottles for decorative arts and crafts projects for children is another option. Simply fill a water bottle with shredded paper and decorate the bottle using paint or markers. By using construction paper and cutting out shapes, they can be adhered to the water bottle. This is only limited by your imagination. The bottle can be a boat, filled with the shredded paper and sporting a construction paper sail, or the bottle can be decorated as the body of a monster who just ate a book.
Using shredded paper as kindling for a fire is a great way to repurpose it should someone need kindling. Keep in mind that shredded paper is light and can be blown up with an updraft in a chimney, so use sparingly. The positive to using it this way is that shredded paper will light easily and the flames will spread quickly, helping to start a fire in a fireplace or fire table.
Shredded paper can be used when planting. Place enough shredded paper to cover the bottom of a hole dug for a plant, then sprinkle fertilizer on top of it. When the plant settles, the roots will have a nutrient-rich foundation that will also attract bugs to eat the paper and create more fertilizer. An added bonus to using shredded paper is that it will soak and harden, giving larger bushes or plants a sturdy foundation.