As real as a Unicorn
The term "no-fee broker" is a contradiction - a marketing gimmick. When an agent helps find your apartment, there's always a fee owed to them. The question is who pays it - you or the landlord? If the landlord plans to pay the fee, the apartment is advertised as "no-fee". When landlords are willing to pay the fee, they'll communicate that to every major brokerage so agents will help fill their vacancies. Most agents in NYC should know about and have access to all the same "no fee" rentals.
Why landlords pay the fee
Paying the fee on behalf of a renter is expensive. Often it's only done when a landlord is desperate to get his or her apartments rented, which can be a bad sign.
Account for the fee in your maximum rent
If you're using an agent but refusing to pay a fee, try dropping your maximum rent to account for the cost of the fee. You'll have more, and perhaps better, apartments to choose from. So what's the catch? Cash! If you don't have money saved up to pay the broker's fee, well then this option isn't for you. But remember not to stretch your budget. Here's help to calculate how much rent you can afford.
Choosing only "No-Fee" listings
The NYC rental market is generally so hot that landlords don't have trouble renting out apartments. This means very few of them are paying the broker's fee on your behalf. So if you're using an agent and limiting your choices to only "no-fee" apartments, you'll have fewer options.