There are plenty of non-FATCA countries but as
@Perry8 already said, most banks sign up for FACTA even if their country didn't.
- Afghanistan
- Albania
- Andorra
- Argentina
- Bangladesh
- Belize
- Benin
- Bhutan
- Bolivia
- Bosnia and Herzegovina
- Botswana
- Brunei
- Burkina Faso
- Burma (Myanmar)
- Burundi
- Cameroon
- Central African Republic
- Chad
- Comoros
- Congo, Democratic Republic of the
- Congo, Republic of the
- Cook Islands
- Côte d'Ivoire (Ivory Coast)
- Cuba
- Djibouti
- East Timor (Timor-Leste)
- Ecuador
- Egypt
- El Salvador
- Equatorial Guinea
- Eritrea
- Eswatini
- Ethiopia
- Fiji
- Gabon
- Gambia, The
- Ghana
- Guatemala
- Guinea
- Guinea-Bissau
- Iran
- Jordan
- Kenya
- Kiribati
- Kyrgyzstan (Kyrgyz Republic)
- Laos
- Lebanon
- Lesotho
- Liberia
- Libya
- Macedonia (North Macedonia)
- Madagascar
- Malawi
- Maldives
- Mali
- Marshall Islands
- Mauritania
- Micronesia
- Monaco
- Mongolia
- Morocco
- Mozambique
- Namibia
- Nauru
- Nepal
- Niger
- Nigeria
- Niue
- North Korea
- North Macedonia
- Northern Cyprus
- Oman
- Pakistan
- Palau
- Palestine
- Papua New Guinea
- Russia
- Rwanda
- Samoa
- São Tomé and Príncipe
- Senegal
- Sierra Leone
- Solomon Islands
- Somalia
- South Sudan
- Sri Lanka
- Sudan
- Suriname
- Swaziland (Eswatini)
- Syria
- Tajikistan
- Tanzania
- Togo (Togolese Republic)
- Tonga
- Tuvalu
- Uganda
- Uruguay
- Vanuatu
- Venezuela
- Yemen
- Zambia
- Zimbabwe
To be more exotic, there are also Abkhazia, Nagorno-Karabakh (Artsakh), Pridnestrovie (Transnistria), Sahrawi Arab Democratic Republic, Somaliland, Tskhinvali (South Ossetia), Donetsk and Luhansk but I wouldn't call them "countries" and banking might be a little tricky.
