From lowest count to highest, here is the range of differing opinions on what makes a country a country, and more importantly, what counts as a ´real´country.
Although the UN is often the default count for people to believe, its not that clear what their official number is. I´ve seen both 193 and 195, since Taiwan and the Vatican have some strange non-member observer status. Then there´s Kosovo, which over a hundred of those member states recognize, but not the UN body. UNESCO, a branch of the UN, has a member list of 195, including Palestine but excluding the Holy See and Taiwan from the UN list, plus 11 associate members.
This pushes the count up to 206, which the National Olympic Committee also has, but they no longer recognise Curacao, Gibraltar, the Faroe Islands, Macau or New Caledonia. Though they used to be part of the International Olympic Committee, they now have to compete through their parent nations (Netherlands, the UK, Denmark, China, France) though the Faroes and Macao are allowed to athletes as their own in the Paralympics.
FIFA says there are 211 registered football teams in the world from different countries (the UK is split into its 4 countries), excluding some UN countries, since not every country in the world has a national men´s football team (ie. Micronesia, Kiribati, Marshall Islands, Monaco, Nauru, Palau, Tuvalu and the Vatican).
Couchsurfing has over 230 countries, and claims to have a registered host in every country in the world. With 2 million users, this is definitely possible, but the truth is its hard to find hosts in countries where the site is illegal, like Iran, where there is only one host, like in Wallis & Futuna, or where the site is nonexistent, like in North Korea.
The highest count is over 300. The Centenary Club, an elite members only group of travelers, counts 327 countries and territories.
If you ask me, the definition of a country isn´t rocket science. If you pass a border or showed a passport, had to apply for a visa, or use a totally different currency and maybe a new language, then you´re probably in a different country. I definitely stand by the fact that every time I went to Greenland, I was not in Denmark, and French Guyana is nothing like France except for the euro currency. I actually think its strangest that everyone can agree to call the Holy See a separate country, but others have more problems with territories and their status. I’m somewhere in the middle, with about 245 countries on my horizon, of which 25 I have left to visit.