Always popular were photos from Africa, such as Ethiopia, where I have spent over two months, but also newly uploaded pictures from Namibia. I have travelled extensively in West Africa and my generally most popular photos from there came from Ghana, Cameroon and Burkina Faso.
In Asia, the historically most popular were from Mongolia but this has been overtaken by Indonesia and Papua New Guinea. The single largest collection of photos is from China, drawn from three trips that in total extended approximately three months.
Countries become briefly of interest to visitors when there has been news - Haiti after a hurricane, Nepal after the earthquake, Burkina Faso, Libya, Mali, or Tunisia after poltical instability.
In general countries with significant diaspora elements appear to attract viewers (Ethiopia, Eritrea, Armenia for example).
Photos from countries that either have many flickr members who live there or those that see many tourists probably for that reason see fewer visitors.
A selection of my photo albums