A basic home insurance New York policy covers perils, which are specifically named risks such as lightning, theft, fire, smoke, wind and explosion. One thing to remember with this type of home insurance New York policy is that any risk that is not mentioned specifically in your policy is not covered. From some insurance companies you are able to purchase special policies that cover the house for all perils except those explicitly excluded by the policy though, such as pet damage. Be sure when you buy the policy, to read and understand every word printed in it, especially in the small print.