Is it legal for a doctor to charge a no-show fee for a missed appointment?

Absolutely it is legal for doctors to charge no show fees.  That time is valuable to them and they could have used it for another patient.  Someone's failure to comply with the doctor's office policy regarding appointment cancellation can lead the way for the office to charge a no-show fee. 

In terms of the amount, it depends on the cost to the doctor (amount he or she would have charged for the appointment).  In terms of the amount, I have seen no-show fees as much as $250.00 and in most states, the board of medicine considers this fee to be a fee dispute between the doctor and patient, and not within the purview or jurisdiction of the board.