Coney Island is the kind of park where when I google for quotations, e.e cummings comes up fifth, along with a photo of Anais Nin standing in Coney Island. Try that with SF Great Adventure or Busch Gardens Tampa.
Certainly, Coney Island has a history not many other parks can compete with. The first amusement venue was built on it's grounds in 1886, making it one of the oldest spots still holding an amusement park in America. In addition, the world's first rollercoaster was built here, as was the world's first looping coaster. If that's not enough, the world's first hot dog was sold here as well. Two of the attractions currently operating, the Cyclone and Wonder Wheel, are 76 and 83 years old, respectively, making them two of the oldest operating rides still standing in America.
The park's history is too diverse & turbulent to discuss here in any great detail. One amusing note, however, is that the park's "heyday" is considered to have been between 1903 and 1911. In other words, the area is considered to have started declining from it's zenith before the older-then-my-grandfather Wonder Wheel was even built. This park has a seriously long "decline period."
For more on the history of Coney Island, these links are quite good resources:
Coney Island History Site
American Experience - Coney Island
Amusement Park History - Coney Island