When appraising a home do you include the finished basement as square footage, or not ?

What State? I think it varies if its counted or not by state or locality. I know Mine isn't. They count "Above Grade" living space here apparently here where I live in Virginia. My basement was finished at time of construction, not later.

Yes, as far as I know, you will have to include it.

Are you an appraiser? If not, why are you asking. If you are asking how to value your home for sale, then yes you would include any such amenities.

For purposes of giving an appraised value of a home, the professional appraiser generally goes by "comps". These are what comparable homes sold for recently.