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.

Map by land area

1900

1960

2000

2050 (UN med. projection)

Information and code for the cartogram algorithm are available on Michael Gastner’s website.

See also this earlier post on visualizing ecological footprints.