Other insurers will ask you questions about your dog's history and will consider coverage on a case-by-case basis. State Farm appears to be dog-friendly and is one example. Though State Farm paid more than $109 million as a result of nearly 3,800 dog-bite claims in 2011, the company does not refuse insurance based on the breed of dog a customer owns. (See: " The $30,000 dog: How a biting pooch costs you.")