As a former mover myself (summer job in high school / college), I can verify that jerz and cabr are on the money with their advice. Yes, moving insurance is largely a ripoff and my boss always loved when customers bought insurance. However, as jerz pointed out, this is usually additional insurance and you get a base level depending on how big (usually by weight) your shipment is. That should be fine for most normal items, but you'll want to avoid (if possible) using the moving company for breakable items (china, glasses) or for highly valuable ones (guitars, Plasma TVs, Picassos, etc.).
If you MUST use the moving company for these things (if you're not driving a car to b-school or if you are moving a great distance), you may want to consider some extra insurance if not already covered by your homeowners insurance. At a minimum, just suck it up and pay the moving company to pack your breakables. As cabro stated, "you're never covered for whatever breaks inside your boxes if you packed them yourself". We called these boxes "PBO"s (packed by owner), and they were [strike]mis[/strike]handled appropriately ...