I watched a show on HBOW tonight about the Soviet Union - USA Olympic basketball finals in 1972 (what a rip!). Anyway, it got me thinking about the Soviet Union breaking up into Russia and a bunch of other countries, Germany coming together, etc. and I wondered -

Just how many countries are there right now and has the number been growing or shrinking?

The US Dept. of State recognizes 191 distinct countries as of January 2001.
Here is a LIST
Oh and Taiwan is in limbo. It kind of matters who you talk to though, some countries recognize as many as 266 countries.

193 - now that East Timor is independent - is probably the safest figure to go with. It depends, you see, on whose list you accept. The American Government, for example, does not recognise Taiwan...as the answer above says, but other countries do. The United Nations does not include the Vatican or Switzerland, though the people of the latter country recently voted to join. Are Scotland, England and Wales three countries or just one as the United Kingdom? And so it goes on.
The figure of 193 includes the Vatican and Switzerland and treats the countries of the UK as one.