You can fly over just about any country in the world though you do need permits for each one. We fly over Iraq and in Iranian airspace all the time. You do need to follow procedures for each specific country. If an overfly permit is not recieved or invalidated (time period expired etc.) then you will have to fly around that country. A prime example is India overflights when operating from the Middle East to HongKong. Flying over means around 8.5 hours flying, going around is over 11 hours.