Your homeowner's insurance covers the cost of your goods while they're in your hands, but not while your movers have possession of them. So if you're using professional movers, even if they have insurance, it may be worth purchasing some additional protection to cover your furniture freight during transit.
Even if you're not purchasing separate moving insurance, it's a good idea to create an inventory of the items you're moving. This will be a useful reference to make sure everything arrives safely at its destination. On your inventory, describe the item, note its approximate weight and estimate its replacement value. For antiques or other much-valued items, it may even be worthwhile to have a friend with a digital camera document the item's condition before being loaded.