That would totally depend on your own financial ability. When you have a job that will pay enough to pay rent, utilities, car payment, insurance, etc, you can be independent of your parents. It's a lot more difficult today than it was when I finally flew the coup at age 20. Back then, rent for a brand new apartment was $170 per month, my car was paid for, car insurance was about $200 per year. Utilities for an apartment didn't include cable and internet (weren't invented yet), didn't have a cell phone payment and a brand new pair of Chucks were about $10. Of course back then, paychecks weren't anywhere near what they are now but the cost of living was a lot more reasonable. I see a lot of 20-35 year old's still living with mom and dad today because they just can't afford to live on their own yet.
I have heard that Americans leave their homes mostly when they are 18. I have always loved this about them. In Iran, where I am from, you only leave your home when you get married, no matter what age you are! It is terrible. Families are super supportive and it makes children never really grow to be independent. When they marry, they get into lots of trouble managing their lives, since it has always been done by their parents and now they have to do it themselves.