Suggest:

      If it is a window unit or a portable, WRITE IT INTO THE CONTRACT under personal property conveyed.   That should prevent any misunderstandings.

Yes, if it's attached, no if it's a portable unit.

The AC unit conveys just like any other attached property...such as the furnace or hot water heater.

An exception would be a portable unit that is not attached to the house except by an easily removable intake vent. Then I would consider it to be an appliance like a cloths washer or dryer or free-standing refrigerator.

As I used to explain to my clients...
Anything that is nailed down, screwed down, or otherwise permanently attached goes with the property. When in doubt specifically address whether it does or does not transfer with the sale.

If a wall unit - maybe not. If it is movable it would fall under personal property. 

If it is its own system - it is real property and transfers. 

California. 

Only if attached and implied when shown to others

If it's in doubt it needs to be mentioned in the contract. If it's a window one that slides in and out of the window or if it's a portable one that can be moved from room to room, it's probably not a fixture.

If you have to uninstall it, it's probably a fixture.

If you can pick it up and walk away with it, it's probably personal property.

Be explicit in the contract, if it's not already boilerplated in.

Yes absolutely Austin in AZ.

A window unit might not be a fixture. Each area defines fixtures differently. A central AC unit is definitely a fixture.

Check your local contract and state rules. I would say yes. And like Fred Griffin said if it is a window unit, write it in to avoid confusion. 

Unless specified window air conditioners would not be transferred with the property

Attached units yes! And that includes through the wall units. If a portable unit or window unit, you want it, put it in the contract.

As with anything, is it attached?

A window unit may not be.

A wall unit built into the wall is

A unit built into the heating system is also part of the real estate.

Though most sellers that do sell homes with window units often leave them behind since most are moving up to a home with central air.

The best answer is "it depends." If you want it, write it in! If you don't exclude it.  The last words we don't want to hear are, "But I thought it was ..."

it all depends.  window unit installed.  maybe.  remove it from the property and you get rid of the problem.  

Central air yes.

Window unit, no.

In Colorado, if you need a "tool" to remove something, it is considered a fixture and included, unless stated otherwise in the MLS.

In our area they would be 'expected' to stay but you'd write it under personal property for your buyers. 

Yes, anything attached to the house is real property including plants and trees.

A Window Unit is still Personal Property

If attached or screwed in, it stays unless excluded in writing at the outset.