Some appliances need an earth wire and some do not.
An appliance needs an earth wire if the case is made of metal. If this is the case then a wire touching the case can make it live so that if someone touches it they can receive an electric shock
If the appliance has an insulating – plastic – case and no exposed metal parts it cannot become live so cannot cause electrocution. The device is said to be double insulated. Double insulated devices carry this symbol of a square inside a square.
Many heating appliance – fan heaters, hair dryers or kettle – are double insulated. These devices MUST be double insulated since they are regularly handled so the cases cannot under any circumstances become live. With a hair dryer this is especially important since these are sometimes used in the bathroom or with wet hands.