There is a great documentary on HBO called, Birders: The Central Park Effect. The movie shows the huge range of birds who live in the park and use it as a stop over on their migratory flights.
If you live in the city or are just visiting you can take full advantage of bird watching in the park. One of the best places to go is the North Woods towards the top of the park. Spending even an hour on the weekend will afford you the opportnity to see a lot of different bird species.