Procure usar o que é chamado de CTE (expressão de tabela comum) (consulte o documento MSDN):
;with cteAppointments as (
select AppointmentID, PersonID, PrevAppointmentID
from Appointments
where PrevAppointmentID is null
union all
select a.AppointmentID, a.PersonID, a.PrevAppointmentID
from Appointments a
inner join cteAppointments c
on a.PrevAppointmentID = c.AppointmentID
)
select AppointmentID, PrevAppointmentID
from cteAppointments
where PersonID = xxx
