2. Blow your nose on it. Using tissues in places with no trash can is a pain. Somehow they always end up tucked in weird places or stuck to an entire load of laundry after being sent through the wash. Bandanas that have been used as handkerchiefs can be machine or hand washed with detergent and hot water, and ultimately take up less space and resources than a box of tissues.
3. Use it for first aid. In a pinch, a bandana can become a sling, a tourniquet, or a bandage. You can fill it with ice to make an ice pack or wrap it around something hot to make a hot pack. You can dip it in water and use it to clean a wound. If you're caught out without a first aid kit, it could save your life, or at least your comfort.
4. Make a bindle (the cloth bundle on a stick you see in stereotypical depictions of hobos). This is actually a convenient way to carry an unexpected load and can be put together on the spot. Find an appropriate-length stick, place your goodies in the middle of your bandana, and tie the corners to the end of the stick. You can also tie the ends to your belt loop, handlebars, or backpack strap to make a pouch. This is great for things you find along the way, or items you don't want to get crushed in your backpack or pocket.
5. Dip your it in water then tie it around your neck, letting the evaporating water cool you off. This works best in dry climates.
6. Tie it over your face outlaw-style to keep dust or sand out of your nose and mouth.
7. Tuck it under your hat to keep the sun off your hat to keep the sun off your neck. Sure, it's not all that stylish, but neither is a sunburn!
8. Clean up yourself, someone else, or your gear. A wet bandana is a great way to do a quick sponge bath in your tent or a public bathroom. It also works great when you need to wash up in a stream that's to shallow to really get in. When you have enough water and privacy for a real bath, use it as a washcloth. You can also use it to wash dishes or clean up spills.
9. Get someone's attention. A red bandana makes a great signal flag in an emergency.
10. Sling a line over a branch you can't reach. Tie up something heavy (a rock, your car keys, a camp biscuit) in the bandana then tie it to the end of the rope. Give it a few swings then toss it over. With any luck you'll be able to grab it on the other side and string up your bear bag, hammock, or clothesline.