In fact, you can buy a home even in a place like New York with less than 20% down payment. In fact, many condos will allow you to make a 10% discount (and sometimes less if you're FHA approved). And there's no fixed amount required for a single-family home. The standard down payment for a New York City condo is 20%.
That said, some condos will be less accepting and not all condos have a minimum down payment requirement. Some new developments in the city will accept payments of 10% or, in exceptional cases, even less. The average down payment for a cooperative apartment in New York is 20% of the purchase price. The exact down payment and financial requirements vary by cooperative building, however, it's rare to find a cooperative building in New York City that allows a down payment of less than 20%.