I'm a firm believer in paying "board". I think once you leave school, no matter what age you are, and you are working then you should contribute.
If still in full time education then I don't agree, you still receive child benefit, tax credit and whatever else people are entitle to, until the age of 19 if in full time education (not including university), so I don't think kids should then pay their parents - even if they have a part time job.
My daughter plans on going to university so I won't have to cross that bridge, but if she comes home afterwards then she'll pay. If she doesn't go then she will pay board, a nominal amount, as I'll want her to save up to move out eventually!!!