Do I need approval from the FAA to fly a model aircraft for recreation or hobby?

No, but your aircraft must be registered if it weighs more than 0.55 lbs. FAA guidance also says that model aircraft should be flown a sufficient distance from populated areas and full scale aircraft, should be kept within visual line of sight of the operator, should weigh under 55 lbs. unless certified by an aeromodeling community-based organization, and cannot be used for business purposes.^{1, 2}