Military wife here, veteran of 4 professional moves (so far). Had damage on 3 of the 4. Lots of good things pointed out above...
1. Valuables. Anything that can't be replaced at any price should be packed by you and moved by you (think family jewelry, fine art, insurance policies, wills, other important paperwork, etc). (Knowing what your coverages are will help you in this decision. We collect antique china, but it's available at Replacements.com. Anything they break they have to buy a replacement piece. Family photos, jewelry, etc. go with me. Always.) Anything that you are planning to move should be put in a separate room and locked off so that it doesn't accidentally get packed. We usually put all of our self-move stuff in the hall bathroom or guest room(after we empty it first) and lock the door so they can't get in to pack that stuff. We also put a sign on the door "DO NOT PACK"
2. We usually keep out a box of cleaning supplies so that when we get to the house ahead of the load, we can clean it before they put boxes everywhere. You'd hate to have to go to Wal-Mart first thing to get the basics. On a related note, we make sure the vacuum is held out to be the last thing put on the truck so we can vacuum the house one last time. As soon as they empty the first room of boxes, we vacuum and close the door. Follow them as they empty the house.
3. We ALWAYS let them pack us. What would take us weeks to do, they accomplish in 2 long days. (I'm a pack-rat with a 3000sf house...you do the math!!) Make sure your cannisters have been emptied of flour, sugar, etc. as they will pack them full if that's how they're sitting on the counter. Empty your trash can or they will move the garbage. No lie.
4. We NEVER let them unpack us. I do have them put the big pieces of furniture in place, reassemble the beds, and unpack the appliances. BUT, what they packed in 2 long days must be unpacked in 1, and they unpack it and put it on the floor and move on. (And as someone else said, the unloading staff isn't always up to snuff, especially if there isn't a local branch of that company where you're moving.) If they unpack you, there's WAY too much stuff lying around for you to move so you can't arrange things, can't clean the cabinets before putting the dishes away, don't have time to decorate or decide where things will go. Potential for lots of breakage... We do make sure all the boxes are in the right rooms and then we tackle it one room at a time...kids bedrooms first, followed by kitchen, then family room, then our room. I feel it's much more manageable this way and I don't have to trip over all my stuff until we have the time to arrange it. (We have had them unpack the clothes wardrobe boxes a time or two...that didn't cause too much chaos and it was nice to get those big boxes out of the way so we had a little more room to move around.)
5. Keep track of all your paperwork. Make sure you read everything you sign. Take special notice of the "damage noted at pick-up" section as they tend to exaggerate this area to reduce claims on the back end. We took pictures (love that digital camera) of everything before we moved so we had proof of condition. Make sure you understand the deadlines and procedures for filing a claim.
6. Always insist on an accurate accounting of the boxes coming off the truck. If you don't have that accounting, you can't prove it is missing!!
Anything else, just ask!
Katie