No -- not those kind of leftovers! I mean the stuff leftover from the newspaper once you get the good stuff out (the coupons, of course!) Sure, you can stick it in the recycle bin and be done with it, or you can get creative. So here is some of the things we do with our Sunday paper minus the coupons:
Use the funny papers as gift wrapping. This is especially good for birthday presents. I never seem to run out of them, so I can wrap as many as I need -- essentially for free since I counteract the cost of the paper with the savings from the coupons.
Make something with paper mache. You could create a pinata for a birthday (goes with the funny paper wrapping!) or create an entire solar system. The cheapest way I know is to water down white glue, with a ratio of about 4 parts water to 1 part glue, and run strips of paper through the glue mix, then lay them onto a balloon. It will take a lot of layers, so be patient. It will also take a long time to dry. If you are planning on making a pinata, be sure and incorporate some sort of hanging device.
Clean windows. Seriously, cleaning glass with newspaper is a great way to get a streak-free, lint-free finish. Your hands might end up black from the print, but your mirrors will be beautiful!
There are a million things you could do with newspaper, and these just scratch the surface. No matter how you use it, recycling in any capacity is better than all that paper going to a landfill.