A significant number of tenants pay their rent with money orders or cash, as opposed to a personal check. If you do this, under New York State law you are legally entitled to a receipt from the landlord, and should ask for one whenever you make a payment in this manner.
In most disputes with landlords, you end up needing proof of having paid the rent. If you paid cash and don't have a receipt, it's your word against the landlord's, and you're essentially out of luck as far as legal evidence is concerned.
Financial institutions charge varying amounts to trace payment of money orders. They differ in how long the trace takes and whether you can do it online. It's faster, easier and cheaper just to get receipts to prove your payments.
It's probably easier to trace a canceled copy of a bank money order than one from the post office, but both of these options take time, so it's wise to get a receipt anyway as validation of payment.
If there's bad blood between you and the landlord, you may want to have a receipt already prepared when you go to make payment, and have the receptionist at the management office sign it. It's still a valid receipt, and you can zip in and out. Just make sure the receipt indicates the period the payment covers, along with the date, amount, address and apartment number.