Depends on what you mean by “country”. The number could be well over 200 (212 I think) if you include San Marino, Vatican city and so on as countries. There are also semi-autonomous places such as Greenland, or countries within countries such as Scotland (which has its own national team and parliament, but is still within the UK borders with Wales, England and N.Ireland). And of course non-recognised “countries” such as The Republic of Northern Cyprus, which is a de facto autonomous territory on a conquered piece of land of a “normal” country.
And then there’s Cascadia.