If the shipping company doesn't offer insurance for personal items stored in the vehicle while in transit (if that's even allowed, per BrenBarn's comment), then you'll want to ship your personal items with a carrier that does offer insurance. Otherwise, let them go uninsured.
As mentioned by Dan, your car insurance likely won't cover personal items in the vehicle.
However, contrary to his note about Homeowner's coverage, personal property loss or damaged in a personal vehicle being moved by transport vehicle is not likely listed under "perils insured against" in your homeowner's policy. They're pretty specific about what is covered and what isn't.
If you want to insure your belongings against damage or theft while transporting them, you will have to ship them with a carrier that offers insurance. (Moving companies, USPS, UPS, FedEx, DHL, etc.)
Operating on the assumption of transport within the US.