Number of Countries Historical Timeline

The trouble is that it's hard to define what counts as a country. I see problems in two directions.

First, you have a layers-of-government question. Each state in the United States has its own legislature and executive, its own court system and its own laws, but we don't consider those countries. Indian tribes are even more autonomous, but most people wouldn't list them.

In the European Union a bunch of countries signed a series of treaties that connect them in various important ways. At what point in that series of treaties did the EU become a country, and France, Germany, etc become mere subdivisions of it?

Second you have recognition questions: Lots of people claim to have countries, and then other people don't believe them. China still claims that Taiwan is still a province in rebellion, and I bet that North Korea has similar claims about South Korea. I bet that you could come up with a couple dozen groups with serious armed forces that claim to be governments, but that most people wouldn't count.

Wikipedia has some interesting information on the growth of the United Nations: http://www.un.org/members/growth.shtml

You might also see if the US government has a list of countries with which it has diplomatic relations.

If the number of countries expanded since WWII, it's probably mostly due to colonies becoming self-governing.

BB: You're definitely right about all the complicating factors. I'd be fine with whatever criteria historians prefer, but I'd really like data that stretches back hundreds or thousands of years and not just through the 20th century.