Tile maps, which visually show areas with unequal areas as having equal area, are, somewhat obviously, appropriate when you don’t want the unequal geographic area to distort the message you are trying to communicate. An example might be if you want to show a variable by congressional districts, which have (roughly) equal populations but variable (spatial) areas.

A couple other ideas with tile maps are (1) to use rectangles of equal shape but different length/width ratios, and (2) to use words spatially arranged and with a variety of properties (font, size, color) to denote a variety of variables.