Good question! Ask Yahoo! had the following answer
About.com's Geography section. The article, titled How Many Countries Are in the World?, was recently updated on December 6th, 2000. It states that depending on the source, the world has either 189, 191, or 192 countries.
The United Nations, which represents almost every country in the world, has 189 members. However, Switzerland and Vatican City have chosen not to become members of the United Nations. Therefore, many people believe the number is 191. But not so fast...
Taiwan ostensibly meets all the requirements of an independent country, but, due to political reasons, much of the world refuses to recognize it as such. Taiwan considers itself an independent nation and continues to push for recognition from other countries, but two of the world's powers, the U.S. and China, have yet to be swayed.
If Taiwan is considered an independent country, as it is by the World Almanac and Book of Facts, then there are 192 countries in the world. It should be pointed out that there are a couple of countries that are heading towards independence: East Timor recently voted for independence from Indonesia, and, if the Middle East peace talks continue in a positive direction, it's expected that Palestine will gain independence in the next few years.
Other sources, such as the CIA World Factbook, list the number of countries as much higher, but these counts usually include territories and colonies like Puerto Rico and Bermuda, which are governed by other countries.
Depending on your criteria and definition of a country, the current count can range anywhere from 189 to 266 or so.