Emporis updated the New York section. According to the database, there are 143 skyscrapers under construction, and 115 planned. I think in the next year or so, we may be the construction capital of North America.
The city has 696 skyscrapers, and 5,813 high-rises once I reduced the number for the unbuilt and only counted complete. Thats a total of 6509.
When all of the current projects UC finish, that will be 6652.
If the current proposals go through, and keep in mind that it will change as a highrise gets proposed every day or so (13 stories or greater), that number will be over 6800. Which will be much higher by the end of 2017 or 2018 as the affordable housing plan and the city continues to boom.