There's also an interactive version of the map that you can use to explore the map in great detail, which you can find here. You can click on any country to display its name and capital (some of them are a bit silly, some unimaginative, some I'm happy with)
I'm not going to go into detail about my design choices for any individual country here, but feel free to ask me about them or complain/comment. In general, in places I wasn't intimately familiar with, I used a mix of existing administrative boundaries and data about linguistics, political leanings (largely derived from election maps) and, where appropriate, ethnicity. In other places, countries are very much predetermined by geography and the population constraints (Japan and Central America are good examples for this).
Technical Process and lessons learned
In the beginning, I started out very much like frayuk presumably did in drawing his map-- I took a big picture of the world, divided into their first-level administrative boundaries (states, departments, regions, länder, and what-have-you) and started coloring over them in using Gimp-- a free photoshop alternative and keeping track of populations in Excel.
When I was done with that, I had something looking like this--it works, but it's fairly crude, and in India and China, where the first-level administrative divisions themselves can have north of hundred million people (Uttar Pradesh has over 200 million!), highly inaccurate because I was just eyeballing shapes.
So, I set out to redo the whole thing in QGIS, a free alternative to ArcGIS, a program dedicated for making maps and dealing with projects exactly like this.
I started out, again, with a map of first-level administrative divisions (a great source for these, as well as second and third level divisions, is GADM.org-- but this time it wasn't pictures, but shapefiles-- electronic representations that list the coordinates of the boundaries of shapes so a program can draw them out.
I colored the countries in once more, adding in more shapefiles for second-level and third-level divisions in India, China, Pakistan and Bangladesh, with an underlying Google Maps layer using the OpenLayers plugin for QGIS.
Once I had my finished layer featuring my countries, I had to figure out how to present them online, ideally interactively. The shapefile was far too large to simply upload to Google Maps directly as a .kml file, so I had to go through the intermediate route of using Shape Escape to upload my shapefile to a Google Fusion Table-- a relatively obscure Google service to manage and manipulate tabular data.
As a technical note, countries that had borders that were so complicated that more than 30,000 points (vertices) were needed to describe them (think of Norwegian or Canadian fjords or Pacific archipelagos) threw errors-- I had to simplify the shapes to have less than 30,000 vertices, which caused the borders to be distorted in some points and some Canadian and Pacific islands to become unassigned to the nations they're supposed to be in-- but it should be relatively obvious in all of those cases.
Countries also had to be matched with a color, which I randomly generated in Excel. The formula
will generate a random hex color value, which can then be matched to the countries in the Google Fusion Table. I manually changed colors where two neighboring countries ended up looking too similar.
I also geocoded the locations of the capitals using this website and added the points to the Google Fusion Table.
If you have any questions concerning either the technical process or why the countries look the way they do, speak up!