Several major news services track the most viewed, emailed, and blog-linked stories of the day or week. Other services allow readers to rate articles.
It would be interesting for them to begin asking users at registration (which many media outlets require, oftentimes for free) for their political views. From this, the same "most viewed" lists could be created, but filtered by political outlook (ie "Most emailed stories by liberals").
I suppose some sources that disingeniously represent themselves as objective would fear an embarrasingly conspicious political bias. But lists as they currently exist do not contain absolute numbers. So what if self-described liberals view five times as many stories in the NYT as self-described conservatives do? Give the stories a relative ranking and this becomes a non-issue.
This would also serve as a useful marketing tool--various businesses or advocacy groups could determine what stories were most likely to be read by the readers they are targeting. Instead of having to aim at the broad readership of the WSJ, advertisers would be able to target specific groups of readers among the subscriber base.