Store and organize little toys. Small boxes with the flaps cut off work great. My hall closet holds lots of cardboard boxes, one has animals, one has Little People castle friends, and another has Little People house friends ( my girls call them their "friends"). A build-a-bear house holds blocks, and a big diaper box cut like a suitcase ( placed on it's side with a large side detached on 3 sides, so that it opens and closes) holds dress-up. Of course all these items are in the closet so that I can control how many and what boxes are out.
Build things. I have already shown you this castle we build out of cardboard rolls and a box. We recently also built a robot with boxes for the torso and head, packaging materials as a hat, and a wrapping paper roll as legs. It was cute, but I disassembled it to use the torso as a shoe storage box before I took a pic.
Make fancy boxes. This is sort-of the same as no. 1, but the finished product is so much nicer and prettier to look at. THIS is an awesome tutorial from Positively Splendid. Her storage boxes are gorgeous!
Use it as a canvas. Running low on paper? Use cardboard. The cardboard that comes under a frozen pizza is perfect for painting or drawing on, or just cut-up a box.
Make music. Of course your kids already sing into the tubes, but you can also put waxed paper and a rubber band over the end to make an even more fun sound. Put rocks or beans in a small box or tube to make a shaker. Another box can be a drum, and pretty soon you've got a band.
Make bulletin boards. I have made two bulletin boards with cardboard as the base. Cover with fabric, string ribbon across the front, add buttons, and hang. Tutorial coming soon.
Make a pencil/marker/scissor/glue organizer. I've got my eyes on this cup holder to transform into an easy to use craft organizer. All it needs are 2 cardboard dividers inside and some decorating. I love that it already has a handle for easy carrying and the base is big so it won't tip over like a pencil cup would.