Not so surprisingly faster than the FAA, apparently, AIG sprung into action to allow drone operators and owners to purchase insurance that covers not only their drone and camera equipment, but also a number of other terrible things that can happen while you're piloting a UAV.
Drone operation can be dangerous, but it allows those of us willing to do it safely get great images at affordable prices for our clients. For those that do this enough, drone insurance is now a possibility that should be seriously considered. AIG's new unmanned aircraft insurance offers third-party liability coverage in addition to covering your non-piloting crew (sliced fingers, anyone?), electronic malfunctions, and even war, hijacking, and terrorism. Plans can be specifically tailored to your needs, but you'll need to talk to an agent to negotiate your plan for you.
Odds are that you'll get a better rate if you can prove you've been doing this for some time or if you have exemption status from the FAA and/or a pilot's license. But anyone looking to protect their equipment and then some should consider insurance.
An Allstate Insurance Agent stated over the phone that Allstate's policy on coverage related to photography varies depending on the use and circumstances, but that these days, whether or not you plan to use drones in your work is a question that is asked could be a reason that they might not cover your business. This is at the start of buying your policy, however — people with existing policies where drone photography is not mentioned are sometimes covered unless there are specific exclusions otherwise.
Meanwhile, a Hiscox agent in an online chat dialogue confirmed that they do not cover anything relating to drones or the use thereof in photography:
...At this time we do not offer coverage for drones and use of those drones in photography ... Full policy documentation is sent out to our clients via email at each renewal. According to our underwriters there are no circumstances that we would cover use of drones under the policy.
As it stands, it appears that AIG's UAV-specific insurance is the best and most comprehensive option for drone operators that really want to be protected.
UPDATE: The relatively well known and well respected insurance company, Hill & Usher, responded to an earlier voicemail, saying that they have offered comprehensive UAV-specific insurance coverage for liability, equipment, etc, related to drone photography for
over "going on" nine years. Various underwriters handle different aspects, but they are one of the "less than one tenth of a percent of insurance companies" offering UAV-specific coverage for your business (now, along with AIG, apparently).