91 year old father allowed to fly a plane again?
What Carlo Felicione has posted is true. Your father must have a Flight Review given by an instructor, examiner, or administrator designee within the previous 24 months of any flight of an aircraft where he is acting in the role of Pilot-in-Command. If there is not another qualified pilot at the controls of the aircraft, your father is acting in the role of PIC. 

The other issue is his medical status. Given the fact that you have said he has not flown in 35 years, I take it that he had either a private (as you stated) or a commercial pilot certificate and not one of the more recently created licenses. There are varying levels of requirements he has to meet and fulfill based on the type of aircraft operations he is conducting.

In order for him to fly as PIC in a powered aircraft without at least a valid unexpired third class medical certificate, he has to have:


Valid unexpired drivers license
Have been in possession of at least a valid third class medical certificate after July 14, 2006.
Document receiving a comprehensive medical exam to the FAA’s standards from any state-licensed physician of his choice within the last 48 months. 
He can not have had his most recent medical certificate or application for a medical certificate denied, revoked, or suspended.
Complete an FAA mandated medical education course on Basic Medical requirements.


In addition...

Title 14 of the Code of Federal Regulations, (Federal Aviation Regulations) Part 61.113 states the following:


  (i) A private pilot may act as pilot in command of an aircraft without holding a medical certificate issued under part 67 of this chapter provided the pilot holds a valid U.S. driver’s license, meets the requirements of §61.23(c)(3), and complies with this section and all of the following conditions and limitations:
  
  (1) The aircraft is authorized to carry not more than 6 occupants, has a maximum takeoff weight of not more than 6,000 pounds, and is operated with no more than five passengers on board; and
  
  (2) The flight, including each portion of the flight, is not carried out—
  
  (i) At an altitude that is more than 18,000 feet above mean sea level;
  
  (ii) Outside the United States unless authorized by the country in which the flight is conducted; or
  
  (iii) At an indicated airspeed exceeding 250 knots; and
  
  (3) The pilot has available in his or her logbook—
  
  (i) The completed medical examination checklist required under §68.7 of this chapter; and
  
  (ii) The certificate of course completion required under §61.23(c)(3).


He may, however, fly an aircraft officially designated and certificated by the FAA as a Light Sport Aircraft as long as his most recent FAA Medical Certificate or application for a Medical Certificate was not denied, suspended, or revoked. And, he must not know or have reason to know of any medical condition that would make him unable to operate a Light Sport Aircraft in a safe manner. Also, he can not fly at night, in Instrument weather conditions, or above certain altitudes (the higher of 10,000 feet Mean Sea Level or 2000 Above Ground Level).


  Light-sport aircraft means an aircraft, other than a helicopter or powered-lift that, since its original certification, has continued to meet the following:
  
  (1) A maximum takeoff weight of not more than—
  
  (i) 1,320 pounds (600 kilograms) for aircraft not intended for operation on water; or
  
  (ii) 1,430 pounds (650 kilograms) for an aircraft intended for operation on water.
  
  (2) A maximum airspeed in level flight with maximum continuous power (VH) of not more than 120 knots CAS under standard atmospheric conditions at sea level.
  
  (3) A maximum never-exceed speed (VNE) of not more than 120 knots CAS for a glider.
  
  (4) A maximum stalling speed or minimum steady flight speed without the use of lift-enhancing devices (VS1) of not more than 45 knots CAS at the aircraft’s maximum certificated takeoff weight and most critical center of gravity.
  
  (5) A maximum seating capacity of no more than two persons, including the pilot.
  
  (6) A single, reciprocating engine, if powered.
  
  (7) A fixed or ground-adjustable propeller if a powered aircraft other than a powered glider.
  
  (8) A fixed or feathering propeller system if a powered glider.
  
  (9) A fixed-pitch, semi-rigid, teetering, two-blade rotor system, if a gyroplane.
  
  (10) A nonpressurized cabin, if equipped with a cabin.
  
  (11) Fixed landing gear, except for an aircraft intended for operation on water or a glider.
  
  (12) Fixed or retractable landing gear, or a hull, for an aircraft intended for operation on water.
  
  (13) Fixed or retractable landing gear for a glider.


He may also seek out getting his glider or balloon rating to fly either of those aircraft without a Medical Certificate. This option is a good one for him. But, it will require home to legally get the ratings through an instructor and Designated Pilot Examiner.

the FAA states in 61.107...


  (2) If the applicant has logged at least 40 hours of flight time in a heavier-than-air aircraft, the applicant must log at least 3 hours of flight time in a glider in the areas of operation listed in §61.107(b)(6) of this part, and that flight time must include at least—
  
  (i) 10 solo flights in a glider in the areas of operation listed in §61.107(b)(6) of this part; and
  
  (ii) 3 training flights with an authorized instructor in a glider in preparation for the practical test that must have been performed within the preceding 2 calendar months from the month of the test.


His last option, as posted by Crossroads, would be to fly an Ultralight aircraft.

The FAA states in Part 103...


  Notwithstanding any other section pertaining to airman certification, operators of ultralight vehicles are not required to meet any aeronautical knowledge, age, or experience requirements to operate those vehicles or to have airman or medical certificates.
  
  an ultralight vehicle is a vehicle that:
  
  (a) Is used or intended to be used for manned operation in the air by a single occupant;
  
  (b) Is used or intended to be used for recreation or sport purposes only;
  
  (c) Does not have any U.S. or foreign airworthiness certificate; and
  
  (d) If unpowered, weighs less than 155 pounds; or
  
  (e) If powered:
  
  (1) Weighs less than 254 pounds empty weight, excluding floats and safety devices which are intended for deployment in a potentially catastrophic situation;
  
  (2) Has a fuel capacity not exceeding 5 U.S. gallons;
  
  (3) Is not capable of more than 55 knots calibrated airspeed at full power in level flight; and
  
  (4) Has a power-off stall speed which does not exceed 24 knots calibrated airspeed.


Here are some overly-simplified examples in a nutshell of what you can do if you have a pilot certificate, appropriate ratings and currency of flight. 


King Air 100 - you need to have a valid FAA medical.   
Cessna 172 - you need to have passed an FAA medical in the last 14 years and have a note from your doctor.   
SportCruiser - you need to be legally able to drive a car.   
Glider or balloon - no medical needed, just a pilot certificate.   
Ultralight - not even a pilot certificate needed.