Today's City Section has a good FYI on New York City birds:
The common pigeon, also known as the rock dove, was bred by the European aristocracy for hunting and eating. Kim Todd, in "Tinkering With Eden" (Norton, 2001), traces pigeons' American arrival to 1605, on a French supply ship, the Jonas, bound for New France. Samuel de Champlain kept pigeons in his newly founded Quebec. More pigeons arrived with English settlers in Virginia...
House sparrows became established here in 1854 when the Brooklyn Institute, hoping to limit canker worms, released several pairs inside Green-Wood Cemetery. In less than a century, their descendants had spread coast to coast.
According to the Parks Department, the most abundant native bird in these parts is the American robin.