For disconnection or transfer of your utilities contact the companies at least two weeks before the move. It will give them enough time to take final readings of water, gas, and electrical meters. It also will save you from being subjected to any late notification charges.
Settle all the bills that are unsettled before the moving day, and recover all the refunds and deposits.
If you are moving across town, you may be able to transfer your services to your new home. However, if you are moving long distances, you will likely be dealing with a new moving company that may or may not charge a setup fee. At the same time you could save few bucks by getting a “bundled” television, phone and Internet service from one company.