My wife and I used to joke about this - we would ask each other "Are we grown-ups now?". Even after getting married, we didn't really feel grown-up.
We are both grown-up now - this happened when my first child was born.
This probably differs between cultures (I'm Scottish and my wife is English).
I definitely wasn't grown up at 19, and I was living in London holding down a full-time job in IT, and living in my own flat.
I'm 26 now, and one difference I find is that things in life aren't quite as exciting as they used to be. It's hard to explain, and maybe it's just me.