Naruto Kyubi
It is not that all the characters of the Naruto anime series wear this headband but intentionally some of the characters wear this headband and some do not wear it. Generally the female characters of this anime series are not required to wear these headbands. The female characters generally wear the headband as an accessory and not as a necessity. For example the character of Ino wears this headband as a belt and the character of Sakura wears this as a headband. The character of Naruto always wears this headband. In fact you will never see this character without the headband on the forehead. Naruto wears this headband as a symbol of pride and honor. There are some other characters such as Rock Lee and Shikimaru that don't wear this forehead protector as a necessity but just wear it. It is believed in the anime that as long as the headband is visible on any part of the body then every thing is alright.
