It seems to be common to memorize the world’s countries using a memory palace, arranging them in some logical order. Harry Lorayne mentions another method in one of his books, where you use the shapes of the countries to link them directly to the world map. (This is the method that I guess most people use for remembering Italy.)
Personally I prefer the latter method since you get a much better overview of everything and can continue using the country shape images to add additional information such as where cities, mountains, rivers, etc. are located.
Here is my personal map of South America:
Argentina just happens to look like a guy with a chicken stick in his eye. To link it to the correct country I imagine that the guy is very angry about the chicken stick (angry = arg in Swedish). Chile looks like a chili pepper, Colombia like a cool cow, Peru like a climber with a small wig (= peruk in Swedish) etc.
Notice how easy it now is to add further info. For the capital of Peru, Lima, I visualise some Lima beans in a bag hanging from the climber’s belt (at the correct location of the actual city). Buenos Aires is located close to the bottom of the angry guy’s eye, so I visualize a small hole there where good air is coming out, etc.
It’s a piece of cake to add ducks (änder in Swedish) walking on the chili and upwards representing the Andes and letting one of them put an acorn behind the ear of Argentina for the highest peak, Aconcagua. 
Finally I’d like to add that many countries have one “representative/official capital” as well as one “administrative”.
My take on this is to add the administrative image as an extra on the official one. E.g. for the capital of Bolivia, Sucre, I imagine the (bowl-like) pot in the middle of the map filled with sugar and then let a peace flag rise from that sugar pile (the administrative capital of Bolivia is La Paz, meaning the peace in Spanish).