Finished basement square footage (even if finished to the same level as the rest of the house) will never be given the same value by an appraiser. The finest basements out there will be lucky to get credited 1/2 the dollar per square foot value as above grade square footage. Most will get a valuation of between $25 - $40 per square foot.
Now many Realtors do not list homes properly so it' not uncommon to see basements included in the total finished square footage of a home improperly. If you have a specific home you're askign aout and will contact me directly through my profile here on Trulia I'd be happy to let you know whether it's being included in the square footage or not.
If any of the basement is below level of ground, that portion of square footage needs to be shown as living space below level and added to the upper level square footage to total the square footage of the home. but it all needs to be finished,heated and cooled. The other element is ceiling height in the basement - at least 7ft - not lower - otherwise, the square footage cannot be counted as part of total square footage of home. I have been told over the years that basements should have access to an exterior door.
As stated a basement is not counted unless it is "finished heated space" . It must have a minimum of 7' ceilings and an exit to the outside.
As also stated it will not be valued at the same $ per square foot as above grade square footage.
Hope this helps,
Basement space will generally carry a much lower value than above grade space.
Bear in mind, any level with any portion below grade is basement level. Any dirt against an exterior wall for a level means that level is below grade.