Are there any official counters which keep a track on the number of downloads of a particular Ubuntu version across different derivatives?
Solution 1:
Ubuntu does not count how many users downloads it. Since Ubuntu does not require registrations and because there are so many non-official mirrors, there is simply no way to count how many times it is downloaded (let alone installed).
According to some assumptions there are ~20 million Ubuntu users worldwide. Mark Shuttleworth, the founder of Ubuntu, announced that Canonical's goal is to get 200 million Ubuntu users by 2015.