The age requirement for youth travelling alone tends to differ with each airline. Although, most airlines say no younger then five or six. They need to be old enough to understand where they are and where they need to be. Usually you can find out by calling or searching on the airlines website.
In the United States you have to be age twelve or older to fly without the supervision of an adult. The child must be supervised by someone, however, so most Airlines will charge a fee to supervise your child for you during the flight.
You can fly as an unaccompanied minor in the United States even when you're 5 or 6. The ticket costs more, but the flight attendants will look after you. You can't buy the ticket yourself, of course.
The age varies from country to country and even from company to company. If you are under age you need to have someone in the company to place a card on you telling you are underage and traveling alone but yes you can still travel alone under 18.