For how long are state and federal aircraft registrations valid?
Federal registration is for three years, according to the FAA (the actual regulations are in 14 CFR 47.40):


  
  Aircraft registration issued due to renewal expires three years from the expiration date of the previous certificate.
  Aircraft registration issued to a new, import, or reinstated aircraft entering or re-entering the U.S. Civil Aircraft Register
  expires three years after the last day of the month in which it is
  issued.
  


State registration - if any - is up to each state so you need to check with the state where the aircraft's owner registered it.