No, I don't ask them to pay me back. Because if one day they ask me to return what they have spent on me, I'll be nowhere.
My parents never ask, as they don't need too. BUT if they were to ask, I'd be like your parents and not expect them to pay it back (unless it was huge amounts) because they did raise me, have helped me out, etc in the past. BUT knowing my parents, if they were to borrow anything, they'd pay it back without my needing to ask them lol.