1. Cash!: Having cash on hand when your movers arrive means never having to leave them with your things while you make a run to the bank. It also means you can, for lack of a better word, bribe them to transport things they normally wouldn't (tools, air compressors).
2. Cold Bottled Water: Even if they carry their own water with them in their moving truck, having water on hand, inside your apartment or home can be a huge blessing and increase their productivity. Plus, they'll be more willing to work for you, no matter what the temperature since you went out of your way to provide something for them (aside from your hard earned money).
3. Dolly: Do you have a great deal of furniture? Lots of large awkward things? Try having an additional rolling or furniture dolly on hand for them to use means things will get done extra fast, just make sure to put tape with a name on it so it doesn't get misplaced when their time is through.
4. A Plan Of Attack: If you've labeled your boxes for certain rooms, them make sure your system is legible and that they understand what's happening before they ever start loading the truck. They might choose to keep like boxes together to make unloading go smoother.
5. A Lack Of Stories: This one is tricky for us as we're far too chatty for our own good, but each conversation outside the task at hand only slows down your help and even if you feel as though they deserve a break, you're still paying them for their services (and usually by the hour) so keep the small talk extra small!
6. Door Props, Codes, Keys: If your apartment building requires any of these things for entry or exit, make sure they have everything they need upon arrival. If you have to continually buzz them in, there's a good chance the system will slow down. Don't forget to notify any doormen if your building has them.
7. Extra Tape/Markers/Boxes: Murphy's Law states that if you are missing any of these things then disaster will happen. Boxes will break, tape will break free and you won't be able to fix the situation. Better safe than sorry — have a few extra supplies on hand.
8. Printed Directions To Your New Place: Even if your movers have a GPS device, having printed directions for them makes life a great deal easier. Try making a run of the route before hand to make sure that the path you'll be taking is as free from potholes and construction as possible.
Do you have anything else to add to the list above? Share your mover tips in the comments below!