Make sure you pack as many of your belongings as possible into boxes as possible. You know your stuff best and if you pack it, it will avoid any potential breakage during the move.
Utilities should be turned off in your current home one day after your move-out date. It is helpful if utilities in your new home are turned on one day before your move-in date.
Back up all computers and have a plan in place for checking e-mail and paying bills online while your computer is in transit.
If you are moving major appliances, make sure that they're cleaned, unplugged, and ready to go. Freezers need to be defrosted and you may need a professional to disconnect gas lines on particular appliances.
Check in with your moving company one last time and confirm that everyone is on the same page. Reconfirm the moving-day arrival time as well as cell phone numbers and last-minute details.