I left home at 19 the fall after graduation, so the subject didn't come up; however, I am thinking my mother probably would not have charged if I had stayed and helped with the house. My father died and brother was married. I was in a big hurry to move to live life, I didn't realize how great I had it at home. Actually, part of the reason for leaving was the depression I felt about not knowing what to do next (NO College) and the dislike I had for the elders in the congregation, in fact I did not like the congregation period, so moving for that reason was good.
Personally, I feel the circumstances dictate if it is appropriate to charge rent to your child, if he is in school, either high school or college than I say no. If he is working making a living wage than yes, and if his or her pay is barely enough to put gas in the car, I suppose some amount just to teach responsibility would be good. But, like another poster mentioned, I think I would give this all back as a gift one day when my child really needed it.
OC