Well, cartograms computed thanks to an algorithm based on diffusion taken from elementary physics.
People tend to like graphical representations of data that factors out variations in population density and at the same time show how many cases occur in each region. There are several approaches and one of the finer ones was discovered and developed by Gastner and Newman , who informally introduce the idea as “On a true population cartogram the population is necessarily uniform: once the areas of regions have been scaled to be proportional to their population then, by definition, population density is the same everywhere… Thus, one way to create a cartogram given a particular population density, is to allow population somehow to “flow away” from high-density areas into low-density ones, until the density is equalized everywhere. There is an obvious candidate process that achieves this, the linear diffusion process of elementary physics , and this is the basis of our method.” In addition, they add notions of boundary of regions (see paper for details). To have quick computations of such maps (seconds to a few minutes), they solve the equation in Fourier space. Then, to actually get any interesting results, one has to set the values for the starting density, some grain size of the regions, and pick any topic of preference for which there are sufficient and reliable data points.
For the myriad of examples freely online at Worldmapper, which were produced using this approach, they took the world and its countries to create almost 600 different maps, each annotated with contextual information. For instance, the proportion of all scientific papers published in 2001 written by authors living in that country, arms exports, influenza outbreaks between 2000 and 2005, etc etc. In the picture above at the start of this post is a screenshot of internet users of 1990 (3 million users) and one of 2002 (631 million), which have changed quite remarkably in both absolute numbers and in proportions. Most data sources used for the maps are from organisations such as UNDP, WHO, and the Worldbank.
The lower numbers in the list of cartograms are about economic indicators, environment, population, disasters, destruction and so forth, whereas in the higher numbers there are all sorts of causes of deaths and religions. See the thematic index for a more targeted exploration or the thumbnails for quick impressions.
The first few maps, e.g. on population, are interactive now, so one can play with zooming in and out. Creating maps at home is apparently possible, too (I haven’t tried that yet); the software is downloadable from Newman’s cart page.
 Gastner, M.T. and Newman, M.E.J. Diffusion-based method method for producing density equalizing maps. Proc. Natl. Acad. Sci., 2004, 101, 7499-7540.
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