For those who are interested in playing by the book, here's a list of some of the New York State dairy and livestock regulations that might effect goat farmers.
Fencing laws -- These are terribly archaic and probably haven't been updated since 1900 but they still hold up in court and apply legally today. This link also has regulations that apply when your animals do property damage on someone else's property and vice-versa.
Dairy regulations regarding the sale of milk and milk products -- These are some complex laws that make it very hard (actually, pretty much impossible) for someone to legally sell raw or pasteurized milk or milk products from their farm.
Of particular interest to goat farmers may be this set of regulations on production, processing, and distribution of milk and milk products.
Here are some specific rules on raw milk sales.
Here's the rules on interstate transfer of goats.
These are the rules for showing goats in the State Fair and County Fairs. I believe these rules also apply to goats that are on public display and exposed to the public (petting zoos, local farmer's markets, etc).
I am looking further into the issue of whether or not goats must be vaccinated for rabies if they are going to be exposed to the public. I have heard people say that it is a law that they must be vaccinated. The problem is that there is currently no vaccine for rabies that is officially approved for usage in goats. There is a sheep vaccine, but most veterinarians won't certify its use in goats because this is an "off-label" usage of this vaccine. It's a catch-22 because if you really do need goats vaccinated, you can't because there isn't a vaccine available. I will report back if I get a good answer from the State Health Department or Ag and Markets.