Because they're permanent fixtures, appliances like air conditioners, oven/stove tops in kitchens and electric hot water systems are usually wired directly into your home's electrical circuits, rather than being plugged into a wall socket.
When you are selling your home, these appliances normally stay behind and become part of the sale. That certainly applies to air conditioners - regardless of the type - mostly because they're installed especially for use in that particular home. Ovens and other large kitchen appliances may or may not be appliances that are basically ‘loose’ items like microwaves are - if you have a special oven you may want to take it with you.
Maximum power requirements
The standard power supply to a home is known as a 'single phase' supply, and is able to supply 240 volts. Appliances that draw 15 amps of current typically need a special plug to do so - although if an appliance draws more than 10 amps of current, it is often wired directly into its own circuit breaker in the switch box anyway.
Appliances that use very large amounts of power (some airconditioners, for example) will require you to install three phase power to help compensate for the load.