How to track popular categories (taxonomy terms) On a website, we want to be able to produce a list the most popular categories (taxonomy terms). We don't want to rank terms by term page  views but rank terms by content page views. When a user views a node page, the score/rank of all terms associated with the node should increase.

I couldn't find any module that provides this feature. As most statistics modules count and aggregate pages views, an acceptable solution would be using a reliable page view counting module that stores its information in the database (or any query-able external datastore). From there, a periodic ranking of the terms' popularity could be computed.

The solution has to work behind a caching reverse-proxy and when Drupal caching is enabled.

Note: we are already using Google Analytics to track traffic.
I don't know of a module which does this but you may be able to do it via google analyitics

token array will allow you to put all taxonomy terms into a custom variable

google analytics reports allows drupal to create reports from GA

So in theory you should be able to do this, I'm not sure how GA handles multiple values for the taxonomy