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)
2. Paul Krugman, Princeton University (1)
3. Ben Bernanke, Federal Reserve Board of Governors (4)
4. Amartya Sen, Harvard University (5)
4. Thomas Sowell, Hoover Institute (9)
6. Mario Draghi, European Central Bank (3)
7. Joseph Stiglitz, Columbia University (9)
8. Alan Greenspan (7)
8. Robert Reich, University of California - Berkeley (9)
8. Walter Williams, George Mason University (9)
11. Daniel Kahneman, Princeton University (NR)
11. Nouriel Roubini, New York University (7)
13. Mark Carney, Bank of England (NR)
13. Simon Johnson, M.I.T. (16)
13. Robert Lucas, University of Chicago (18)
13. Jeffrey Sachs, Columbia University (16)
17. Brad DeLong, University of California - Berkeley (23)
17. Peter Diamond, M.I.T. (19)
17. David Friedman, Santa Clara University (19)
17. Robert Merton, M.I.T. (19)
21. Dean Baker, C.E.P.R. (NR)
21. Gary Becker, University of Chicago (25)
21. Mervyn King (19)
21. Greg Mankiw, Harvard University (25)
21. Raghuram Rajan, University of Chicago (NR)
21. Robert Shiller, Yale University (23)
21. Vernon Smith, Chapman University (NR)
21. Lawrence Summers, Harvard University (14)
29. Daron Acemoğlu, M.I.T. (NR)
29. Olivier Blanchard, I.M.F. (NR)
29. Tyler Cowen, George Mason University (25)
29. Esther Duflo, M.I.T. (NR)
29. Steven Levitt, University of Chicago (25)
29. Thomas Sargent, Seoul National University (NR)
29. Michael Spence, New York University (29)
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 2012 list.
Here is the original 2011 list.
Here is the first 2011 list (August 2011).