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.