Does a private pilot certificate require a certain number of ground school hours?
For training conducted under 14 CFR 61 there is no requirement for groundschool.  The only requirements are that you take and pass written tests, but how you prepare for them (formal groundschool, self-study, etc) is completely up to you.  You will need a recommendation from a flight instructor to take a written test, so your preparation method and readiness for the test will be evaluated before you are allowed to take it.

The only exception to the above statement is knowledge tests for airline transport pilot certificates with airplane multi-engine class ratings taken after 31 July 2014.  These written tests do require specific groundschool training minimums, which are specified in 14 CFR 61.156



If you are instead training under 14 CFR 141, your school has a specific curriculum and examination authority approved by the FAA.  The specifics of your program will dictate what groundschool is required to take the relevant written exams.  The groundschool aeronautical knowledge baseline requirements are specified in 14 CFR 141 Subpart F.  For a private pilot certificate with an airplane category rating, these requirements are:


  
  35 hours groundschool training in
  
  
  Applicable Federal Aviation Regulations for private pilot privileges, limitations, and flight operations;
  Accident reporting requirements of the National Transportation Safety Board;
  Applicable subjects of the “Aeronautical Information Manual” and the appropriate FAA advisory circulars;
  Aeronautical charts for VFR navigation using pilotage, dead reckoning, and navigation systems;
  Radio communication procedures;
  Recognition of critical weather situations from the ground and in flight, windshear avoidance, and the procurement and use of aeronautical weather reports and forecasts;
  Safe and efficient operation of aircraft, including collision avoidance, and recognition and avoidance of wake turbulence;
  Effects of density altitude on takeoff and climb performance;
  Weight and balance computations;
  Principles of aerodynamics, powerplants, and aircraft systems;
  If the course of training is for an airplane category or glider category rating, stall awareness, spin entry, spins, and spin recovery techniques;
  Aeronautical decision making and judgment; and
  Preflight action that includes—
  
  
  How to obtain information on runway lengths at airports of intended use, data on takeoff and landing distances, weather reports and forecasts, and fuel requirements; and
  How to plan for alternatives if the planned flight cannot be completed or delays are encountered.