Sam inherits the car following Dean's death in the series finale. The Impala remained with him until his old age. It is not known where the car went after Sam's death, but it may have been inherited by his son.
After nearly getting caught by the feds and Victor Henriksen in 2X12: Nightshifter After escaping prison in 2.19: Folsom Prison Blues, the boys loose the original Kansas plates in favor of Ohio ones because they know the cops and FBI are after them.