I've asked my insurance agent about covering various items in my house and she said they are all just covered under my general policy, which means any goods in my house that are damaged (not by pets) are covered no matter the cost. So.. you are moving something expensive, drop it and break it, it's covered. If it's manufacturer defect, it's not covered.. (you of course wouldn't want to file too many claims, and especially wouldn't make sense if the value is less than your deductible)
If you tank explodes and you have hundreds of gallons of water worth of water damage, your basic homeowner policy should cover that.. these all vary state to state and company by company, but by and large, it's like if you have a pipe leak or water heater, they cover the damages, a fish tank is no different. -whether or not they'll cover the cost of replacing the tank itself I don't know, might depend on if they consider it a manufacturing defect. but any equipment damaged from the tank leak should be covered.
livestock you wont find coverage for in the US, but like biomek found, if any kind of pets need temporary living space, most major insurance companies will cover those costs, whether it's a dog, cat, or fish..
Best bet is to talk to your insurance company and find out what they would/wouldn't cover.