Here's my list (in rough order by when I first visited them; ones in parentheses are considered separate by the Traveler's Century Club):
USA (Lower 48, Alaska, Hawaii)
Canada
Mexico
UK (England/Wales/N. Ireland/Scotland)
Germany
Austria
France
Luxembourg
Spain
Portugal
(Gibraltar)
Morocco
Andorra
Monaco
Italy
Vatican
San Marino
Switzerland
Czech Republic
Poland
Hungary
Slovakia
Lithuania
Latvia
Estonia
Finland
Russia
(Åland Islands)
Sweden
Norway
Denmark
Netherlands
Belgium
Ireland
Croatia
Slovenia
Romania
Bulgaria
Turkey
Greece
Australia
(Puerto Rico)
Singapore
Malaysia
Thailand
Myanmar
Laos
Cambodia
Vietnam
Colombia
Peru
Japan
Panama
Uruguay
Brazil
Paraguay
Argentina
Israel
Jordan
Egypt
India
Chile
United Arab Emirates
Qatar
Bahrain
Kuwait
Oman
South Korea
North Korea
China, People's Republic of (Mainland)
China, Republic of (Taiwan)*
(Hong Kong)
(Macau)
New Zealand
South Africa
Zimbabwe
Zambia
Swaziland
Lesotho
Namibia
Botswana
Algeria
76 by standard count*; 86 by TCC count. All have been actual visits, not just airport layovers, although five (Myanmar, Laos, Egypt, North Korea, and Lesotho) are somewhat tenuously counted, as I can't claim to have had a visit of any significance to those places (yet!).
Edited to add one of the nicer maps I've seen:
jackal's Travel Map - TravBuddy Only 37%?!
*I recognize that Taiwan is not considered a separate country by definitions such as the UN+3 and other conservative definitions, but in my mind, it absolutely counts as a separate country.