There are a couple of common ways to count countries. You can use whatever rules you like. Two common ways are to count only in the UN (193 Member States) but these leave out places like Taiwan which is certainly its own country. It also leaves out Palestine and Vatican City which are permanent non-member observer states. Call these 196 countries the UN+3.

Places like Western Sahara, South Ossetia, Abkhazia, Northern Cyprus are recognized as countries by some UN countries.

Another popular list is the Countries & Territories list of the Traveler’s Century Club (329 total). This list counts places like Puerto Rico that are not contiguous with the mother country separately. For countries not on both lists, I have designated them with an asterisk. I do not count countries where I never left the airport.

Atlantic Ocean

• Bermuda*
• Falkland Islands*
• Iceland

Europe

• Austria
• Belgium
• Bosnia & Herzegovina
• Corsica*
• Crete*
• Croatia
• Czech Republic / Czechia
• Denmark
• England (United Kingdom)
• Estonia
• Finland
• France
• Germany
• Gibraltar*
• Greece
• Greek Aegean Islands (Cyclades, Dodecanese,
  Northern Aegean Islands)*
• Hungary
• Ireland
• Italy
• Liechtenstein
• Luxembourg
• Malta
• Monaco
• Netherlands
• Norway
• Poland
• Portugal
• Russia
• Slovakia
• Slovenia
• Spain
• Sweden
• Switzerland
• Türkiye (Turkey)
• Vatican City

North America / Central America

• Alaska*
• Belize
• Canada
• Costa Rica
• Guatemala
• Mexico
• Panama
• Prince Edward Island*
• United States of America

Caribbean

• Antigua & Barbuda
• Aruba (Netherlands Antilles)*
• Barbados
• British Virgin Islands*
• Curaçao (Netherlands Antilles)*
• Puerto Rico*
• St. Lucia
• Sint Maarten (Netherlands)*
• The Bahamas
• U.S. Virgin Islands*

South America

• Argentina
• Chile
• Ecuador
• Uruguay

Africa

• Botswana
• Egypt
• Morocco
• South Africa
• Tanzania
• Zambia
• Zimbabwe

Asia

• Cambodia
• China
• Hong Kong S.A.R.*
• India
• Japan
• Macao*
• Singapore
• Taiwan
• Thailand
• Vietnam

Pacific Ocean / Oceania

• Australia
• Galapagos Islands*
• Hawaiian Islands*
• New Zealand

Middle East

• Israel
• Palestine
• Jordan

total: 67 UN+3 countries, 85 Countries and Territories