Depends on where you're located. At the very least you should get yourself some 3rd party public liability insurance in case it decides to fail and drop on someone's head or indeed someone.
Some household policies will cover in the event of theft or loss and some will also include accidental damage which would include damage incurred due to an engine failure etc. You would need to check with your insurer that this eventuality would be covered by your individual policy and state that it would be for accidental loss whilst flying a quadcopter.
Make sure you keep original purchase receipts etc as proof of ownership etc.
Hope this helps
Bmews