I don't think that old cards with zero balance hurt your score. It helps you in two ways-
- It enables a long credit history.
- It increases the amount of available credit. So it will prevent your debt to credit limit ratio going high.
However, you might like to close these accounts to avoid fraudulent activities on it. In that case you may ask your creditors to close the account. If you do not know where to contact at all, dispute the item with credit bureau. If no information of your creditor is available, bureau will remove it from your report.
FYI, if you chose closing the accounts, do not do it all on a sudden. It will instantly increase the debt to available credit ratio instantly and that might be considered negatively.
Hope other forum members might include some more points here.