I'm working on building dot density maps of South Africa using census data. Below is an example of what I'm talking about. Each dot on the map shows 100 people living in Tshwane, the municipality in which I'm currently living. If you can then calculate "catchment" areas for each clinic (the simplest way is to use the shortest Euclidean distance by creating a Voronoi diagram), we will be able to estimate the total number of people served by each clinic. This information, combined with information we have about health outcomes and financial resources of each clinic, will help identify those clinics with the highest burden and fewest resources.
This map was created in R using the dotsInPolys function (which is part of the maptools package) and ggplot2. For a good example of how to build these types of maps in R, check out AnthroSpace's tutorial, Dot Density Maps in R.
In researching these types of maps, I've seen other people create massive dot density maps that are color coded by ethnicity/race. Adrian Frith created a great dot map of South Africa. Below I've embedded a similar map made by the Cooper Center. I'm reminded of the Facebook connections map, in that you can clearly visualize the roads, boundaries and the topography of the entire US, even though the only thing that is mapped is dots - there are no lines in the entire map.