Although I do not mind knowing more about how Digg, Reddit, etc. work and what options they offer, this thing is probably so far the one least likely to be of personal use to me. While I did a bit of exploring, most of the sites showing up as popular are ones I would either easily find in the headline page of a news site or ones in which I wasn't personally very interested. Newsvine was the site on which I found the articles of most interest to me. I think that for me personally, using these sites would not be how I would want to spend my time.
Professionally, I now know to point patrons to sites like these if they are looking to see what stories, sites, photos, etc. are popular--and I could see the use of occasionally glancing at them myself to be aware of what's popular, or perhaps using them to put together book displays on currently popular topics.
Except for this assignment, I don't know that I have read an article based on popularity--if it's one I've been interested in, I've read it and if it's not, I haven't. I have noted that ask.com's news page has fairly recently re-organized itself to include popularity rankings and links to many articles, blogs, and images which pertain to each of its top stories.