Any mountain biker worth his dirt likely has a garage corner filled with worn out tires and bike tubes that have been patched a few too many times. Throwing them out seems wasteful, but the pile is threatening to take on a life of its own. Not to fret; there are plenty of uses for that old rubber that will actually make your ride better.
Nothing ruins the glean of a shiny new whip like that first "ping!" of a rock on the middle of your downtube. In order to prevent those nasty dents and dings, and to give your frame a little padding should you actually slam into a large inert object (like a boulder), cut out roughly a foot-long section of an old tire and use a few zip ties to secure it to the frame. Make sure to mount it as close to the bottom bracket as you can, while watching for clearance for your front cranks.
Another likely culprit for cosmetic damage on your ride is the chainstay, which is liable to get scratched to hell by a slapping chain. Take an old inner tube, cut it in half, and make a single cut length-wise down the whole thing. Starting near the front cranks, start wrapping the inner tube around the chainstay, making sure to spread it out so that there are as few gaps as possible between the wraps in order to maintain a consistent thickness. Grab a roll of electric tape, which holds together better in wet or soggy conditions, and tape off the front. Cut off the tube once you've wrapped all the way to the end of the chainstay, and tape that off.
Our boy Squirrel over at Bike Magazine takes care of the real instruction here. For riders in the Pacific Northwest or East Coast riding in perennially wet conditions, the mud flap made from an old inner tube is an increasing sight. Cut out a section of inner tube about the length of your front fork's travel, poke holes at each of the four corners and one in the middle of the bottom edge, and zip tie them to the fork. Notice that Squirrel installs one more zip tie that pulls the mud flap towards the front of the fork so it doesn't fold back and get caught in the tire under heavy compression.
Strap or Tourniquet
Cutting up an old tube into a few long strips and throwing them in the bag is a good strategy for a host of DIY fixes, be it a busted backpack, loose equipment, or even a tourniquet in more dire situations. Inner tubes are super strong, very elastic, and will hold their tension better in wet situations than any tape will.