When moving to Dubai it is worth noting that most rental properties come with the minimum or no white goods (cookers, hobs, refrigerators, washer/dryers) but usually it is not cost effective to ship these goods over as they are very cheap to purchase in Dubai.
If an apartment or villa is advertised with partial white goods it will be a built in cooker/hob. The space allocated for cookers also seems to vary in properties so if you ship a cooker over it may not fit the allocated space and you will end up with a spare cooker sitting in the garage gathering dust!
The other point to note is that the voltage is is not compatible with electrical goods from the USA and Canada, but is compatible with Europe, including the UK, South Africa, New Zealand & Australia. The voltage in Dubai is 220 V. If you have a favorite washer/dryer or fridge that you really want to bring with you then you can buy a transformer or convertor.
Plug points in Dubai are the 3 pin type however, it is worth noting that many appliances you buy still come with 2 pin plugs but adapters are easily available.
Electrical goods are available to buy in shops such as Carrefour, Geant, Sharaf DG, Better Life etc and are very reasonably priced and can be delivered and installed in your home within a couple of days.
Example of Cost of Basic White Goods
Washing Machine AED 900
Family size Refrigerator AED 1000
Dishwasher AED 1500
Microwave AED 200
Cooker AED 1200
However, it is worth noting that Dubai is a very transient society and some great bargains can be grabbed on white goods on sites such as Dubizzle, local forums such as Expat Chat and supermarket notice boards.
Most homes have water coolers which can be purchased very cheaply and bottled water is delivered to your home for approx. AED 9 per 5 gallon bottle. Many expats moving to Dubai may have been used to the refrigerator with water/ice dispensers which can also be purchased here but these are generally hooked up to the water bottles rather than the mains water supply due to the inconvenience of drilling through walls etc.
If space permits it is worth buying two refrigerators (one to keep in the utility area or garage) as it is always handy to have an extra place to keep drinks cool. I would also recommend buying a chest freezer as you will soon find that you have your favorite store to buy bread, meats etc which may not be local to where you live so it is worth stocking up!