How do I tell ATC that I don't have a transponder?
From the AOPA:


  Flying into a Mode C Veil Without a Transponder  
  
  For flying into a Mode C veil without an operable transponder, the
  pilot needs to telephone the appropriate radar facility for the Class
  B airspace and ask for permission to make the flight. Upon agreeing to
  conditions (including direction of flight and altitude), the pilot
  will be given a code number that he will mention to the controller
  upon initial radio contact. This is the same procedure that a pilot
  with an inoperative transponder/encoder would use to fly in or out of
  the Mode C-veil airports for avionics repair.
  
  The situation may be slightly different if the pilot is landing at a
  satellite Class D (towered controlled) airport within the veil but
  outside of Class B airspace. The approval is still given by the
  controlling radar facility via telephone. The radar facility may still
  issue the code number but may only require the pilot to contact the
  tower in the Class D airspace.
  
  NOTE: You should not expect approvals at the busiest of Class B
  airports during their peak times or under difficult weather
  conditions, but if this telephone procedure can expand the utilization
  of your aircraft occasionally, then by all means, phone to find if you
  can "fit into" the system.