I headed off to college when I was 18yo. I usually came home for the holidays, but I spent the summers on my own. So I guess that my "official" answer is 18.
My younger brother, on the other hand, had to be asked to leave my parents' home when he was in his mid-20's. He went off to college when he was 18, but he was lacking in the skills to socialize with other students, and he soon dropped out and went back home to live with our parents. The ironic thing is that my parents now share a duplex with him. So I guess he's still living with them in his 40's.