At the time of writing, eZ publish does not have functionality that takes care of storing and presenting statistical data related to page-views, downloads and such. (However, the search system has built-in support for search-statistics.) You could make a simple template operator that did the job, and/or a custom table in the database that would be updated every time a download is initiated, etc. Any way, you would have to do this yourself.
Thank you for your quick answer Balazs! Good to know this, so I can go at work now without the pain that I could find such a function in eZp a few weeks later ;)