UAE Post offices are run by Emirates Post (EmPost).
Mail delivery is to PO Boxes only, there are no street deliveries by Emirates Post, however, courier companies such as Fedex and DHL do deliveries to home and office addresses. Empost also have a courier delivery service (Mumtaz?). Most people working in the UAE have mail delivered to their company's address, which usually gets collected daily and delivered to the employee.
Post Office boxes cost about 150-200 dhs rental per year. Companies or individuals can apply for one (you'll need a residence visa and/or trade licence). Application for a new PO Box can be made anytime but renewal is fixed in January of each year.
Contact Emirates Post
Headquarters at Deira Main Post Office, PO Box 99999, Dubai UAE
Telephone +971-4-2622222, fax +971-4-2662929
Call Center telephone +971-600-599999, fax +971-4-3340333
Most post offices are open 0800-1400 Sat-Thu, some of the larger ones are open evenings also from 1600-2200 or all day from 0800-2000 or 1000-2200.
The Dubai Airport Post Office is open 24 hrs per day (but is after you go through passport control).
If you know of any other 24 hour postal service locations, please reply here, thanks .