You need to be a bit more specific in how you define radical change. The United States has not ever changed constitutions, and has a remarkable continuity in governmental institutions, yet our governmental system has radically changed. Marbury vs Madison alone was a seismic shift in the Supreme Court's, and the judiciary in general's, relationship with the legislative and executive branches at all levels of power.

By some definitions San Marino might count. San Marino certainly claims to be the world's oldest surviving Republic, and its founding documents were written in 1600. On the other hand, it has been occupied, most recently in 1944, by the Germans. It's status as an independent nation at certain points in its history is also fairly debatable.