Cartograms, because they distort our normal view of things, are wonderfully rich research and teaching tools. A distance cartogram shows relative travel times and directions within a network. An area cartogram is a map in which some variable is used instead of the land area in each polygon to compute the size of that polygon. Many of us remember using graph paper to make rectangular area cartograms as undergraduates (but perhaps I am dating myself). Today, one can use Web GIS and desktop GIS to create cartograms. For example, nearly 700 variables can be mapped on www.worldmapper.org, and the data can be downloaded as Excel spreadsheets and analyzed within ArcGIS.
To dig deeper and make your own cartograms, with the ability to do bivariate analysis within a GIS environment, use the ArcScript cartogram tool that Tom Gross in the ESRI Applications Prototype Lab created, on: http://arcscripts.esri.com/details.asp?dbid=15638. How can a GIS, which focuses on the accurate spatial representations of features, be used to create cartograms? Try this script and find out!