Comparing economists is a bit like comparing apples and oranges. There is so much diversity in the topics that they approach, and different approaches that they take. Still, it can be quite fun even if ultimately meaningless.
I started entering all the living economists names that I could think of into Google Trends to see who is the most searched for name at Google in 2012. I think it's an interesting addition to the ways of ranking economists because it shows searches and general awareness. Here are my results:
Top Economists of 2012:
rank. name, institution (rank last year)
1. Nate Silver (NR)
4. Thomas Sowell, Hoover Institute (9)
8. Alan Greenspan (7)
13. Mark Carney, Bank of England (NR)
13. Robert Lucas, University of Chicago (18)
21. Mervyn King (19)
29. Thomas Sargent, Seoul National University (NR)
The rankings were calculated on December 31, 2012. Elinor Ostrom was removed from this list due to her death this past June. She will be missed and remembered. There are also (as ever) a number of great economists that unfortunately have names that are not the number one or obvious google search. That list includes John Taylor, Kevin Mitchell, Robert Hall, Justin Lin, and others.
Here is the original 2011 list.
Here is the first 2011 list (August 2011).