Mark Newman (see previous post Another world population map) has used his cartogram technique to make a series of sharp cartograms of the world (smoother than these rougher cartograms), some of which are shown below (land area, population, GDP, and GHG emissions):
This approach was used to create the simpler Worldmapper Project collection of cartograms. A series of their population cartograms are showed below.
Information and code for the cartogram algorithm are available on Michael Gastner’s website.
See also this earlier post on visualizing ecological footprints.