h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

You are physically adult, when your body stops growing.

That doesn't automatically mean you're fit to stand your 'man'.
Thus there are laws to protect youths, respectively to protect society.

In western countries, I think, it takes longer to become an adult, because scholar education alone takes a long time, and when you're finished with school, you don't (usually) know much of the real life (that is: finding a life-partner, grow children, live with them, bear responsibility ...).
One has to learn to make one's own decisions, and then cope with them, good or bad. So, one grows with his/her's tasks.

There is naturally no definite age, one becomes adult. It depends mostly on the life experiences one makes, or is forced to make.

When I've been to India, it seemed to me like a big kindergarten.
The people there seemed to live only for the moment, like children. I envied that, and had to see how 'adult' I already became, and decided not to loose more of my 'childishness'.
But it's hard, when you're back at work for example, to act as you like. You have to fullfill certain standards.
You have to behave like an adult, you get used to this behaviour. Then you maybe grow up your own children and see what you have already lost, recognizing yourself in your kids, as you once used to be.

So my advise to all youths:
Enjoy not being adult! The youth is oh so short!