Accidents can happen when you least expect them or worst, when you are not prepared. This is why it pays have have a good policy to look over your stuff, especially you are moving as road accidents, bumping and such are most likely to occur thus your previous belongings and household goods are facing a high risk.
Your moving company may be responsible for your stuff but you need to be aware that the current rate is just $0.30 per pound for local as well as state to state moves. Considering how light most appliances are these days, its either your brave enough to take the risk or stupid enough to not take extra coverage for your items.
You may have home owner’s insurance or renters insurance and yes they cover your household goods. But the catch here is that they cover for them if they are inside the house, once its in the possession of the mover’s the home owner’s or renter’s insurance are just not applicable anymore.