Keep things together.
Insist on keeping things together when you or the movers are packing boxes. Keep bookends with books, light bulbs with lamps, and extension cords with appliances. Small, loose parts can be attached to the item they belong to with tape or placed in small envelopes -- to keep picture hooks with pictures, shelf brackets with a bookcase, a special wrench and bolts with the wall unit. Keep larger corresponding items (such as a cable TV cord) in resealable bags, and tape these to the underside or back of the item. As a backup, have a "Parts Box" open on the kitchen counter and fill it with cables, cords, parts, pieces, brackets, or nails that are removed from any items of furniture. Keep this box with you, or mark it well with a rainbow of colored stickers so it can be easily located on move-in day.
Anything you can pack ahead will save you time on moving day. If it's summer, get your winter clothes out of the way. You don't really need 5 radios or TV's around your house for the last few days there. Box up your shampoo and extra toothpaste and live out of a travel cosmetic case for the last week or two. Pare down cooking utensils and food supplies to bare essentials. Wastebaskets can also be packed (put things in them!) while you switch to using plastic grocery bags (hang them on a cabinet door or door handle to collect trash.)
Consolidate cleaning supplies.
If you must clean your old place after moving out, put together a kit of basic cleaning supplies and rags. Clean anything possible ahead of time (the inside of kitchen cupboards, the oven, windows, etc.), and if possible, vacuum each room as movers empty it.
Use your luggage.
Fill luggage and duffle bags with clothing, sheets, towels, and paper goods. Even for local moves you'll be able to quickly spot your navy suitcase holding your favorite sweaters, whereas "Box #189" might remain elusive for days.
Safeguard valued items.
It's a good idea to keep valuable possessions, such as silverware, collections, or antiques, with you. If you have a long move and no room in your car, bury the items in a box titled "Misc. from kitchen pantry". Either way, check your homeowner's insurance to see how you are covered during the move, and if you need additional insurance from the mover. Also, find out what paperwork (receipts, appraisals, and photos) you might need to file a claim in case of loss.
Keep important papers with you.
Your list of "important" papers might include: birth certificates, school records, mover estimates, new job contacts, utility company numbers, recent bank records, current bills, phone lists, closing papers, realtor info, maps, and more. Don't leave these with the mover. Keep them with you!
Use brightly colored storage tote boxes, one for each person. Let each family member fill theirs with items they'll want 'right away' in the new home -- a set of sheets, a towel, a couple of extension cords, a phone, nightlights, address book, pens and paper, keys, kleenex, and travel cosmetic case, and so on.
Moving may not be the most fun you've ever had, but planning ahead will go a long way toward making the process bearable.