For me there are two use cases when I am interested in the popularity of a given application or an application version on Ubuntu:
- There is a choice of several similar applications. Before I install one of these I would like to know which one is the most popular.
- To continue developing I get quite some motivation impulse from knowing that people actually do use my application.
Other than the Ubuntu Populary Contest I am not aware of any other service to tell me. Sadly Popcon Ubuntu is rather out of date lately (see bug #1067227 and more). Alternatives listed in answers to "Tracking the popularity of a package over time?" are even more outdated.
When an application source or a DEB package is published on Launchpad we can see the download statistics of this package in the "Download project files" section, but this does not cover installations through a ppa, or when people installed an application from the repositories (which will be the usual case).
Is there any other way I may have missed to find out about an application's popularity?