Get copies of any significant medical and dental records you may have. This will save time when you register with a doctor / dentist in your new location.
Pay off any outstanding loans. Banks will otherwise freeze your accounts until they have been cleared. It is not possible to clear a loan with frozen funds.
If you are leaving Dubai during the academic year, request for a year to date school report.
Notify your landlord, particularly if leaving mid contract discuss with your landlord as there maybe an opportunity to sub let or even break the contract.
Visit DEWA and phone companies to settle your accounts. Remember you have paid a deposit to both these companies upon arrival.
Arrange for DEWA disconnection. Bring your residency visa with you.
If you employ a maid, upon leaving her visa will either need to be transferred to her new employer / sponsor or will lapse with your residency visa and arrangements made for her flight home.