The Aldiko app has now been downloaded 20 million times. Considering that this does not include premium purchases or pre-installed versions of the app, that is an impressive accomplishment.
Aldiko has a far larger install base on Android than either Barnes & Noble or Kobo, a detail I noted when Aldiko reached 15 million downloads in September 2013, and they're not the only indie reading app to best the majors. Moon+ Reader also reports downloads in the 10 million to 50 million range (according to Google Play).
Aldiko and Moon+ are two of the most popular reading apps on Android, second only to the Kindle app - and of course Google Play Books. But given that Google has arranged to pre-install Play Books on nearly all certified Android devices (I think it's a contract requirement), I'm not sure it's reasonable to include Google when looking at installs as a popularity contest.