ON DELETE CASCADE is fine, but only when the dependent rows are really a logical extension of the row being deleted. For example, it's OK for DELETE ORDERS to delete the associated ORDER_LINES because clearly you want to delete this order, which consists of a header and some lines. On the other hand, DELETE CUSTOMER should not delete the associated ORDERS because ORDERS are important in their own right, they are not just attributes of a customer.
One way to think about this is: if I issue DELETE X and it also deletes Y, will I be happy or unhappy? And if I issue DELETE X and am told "cannot delete X because Y exists" will I be glad of the protection, or irritated at the inconvenience?