Residents of which countries are currently allowed to enter Japan?

I would suggest that this is a total exclusion on travel and omissions are errors and not intentional omissions, given that the list for prohibited countries is pretty darn complete - but the thing which sealed it for me is that countries where COVID-19 is eliminated from the population-at-large is on that list, for example New Zealand.

I can also find no scheduled direct flights between Fiji and Japan currently, meaning that if you travel from Fiji to Japan you will almost certainly transit through one of the other countries on the list, which would bar you from entry.

Some other countries not on the list which also don't have direct flights to Japan:

• N Korea
• Taiwan
• Greenland

The current list is:

Afghanistan, Albania, Algeria, Andorra, Antigua and Barbuda, Argentina, Armenia, Australia, Austria, Azerbaijan, Bahamas, Bahrain, Bangladesh, Barbados, Belarus, Belgium, Bolivia, Bosnia and Herzegovina, Botswana, Brazil, Brunei Darussalam, Bulgaria, Cameroon, Canada, Cape Verde, Central African Rep., Chile, China (People's Rep.), Chinese Taipei, Comoros, Congo, Congo (Dem. Rep.), Colombia, Costa Rica, Cote d'Ivoire, Croatia, Cuba, Cyprus, Czechia, Denmark, Djibouti, Dominica, Dominican Rep., Ecuador, Egypt, El Salvador, Equatorial Guinea, Estonia, Eswatini, Finland, France, Gabon, Georgia, Germany, Ghana, Greece, Grenada, Guatemala, Guinea, Guinea-Bissau, Guyana, Haiti, Honduras, Hong Kong (SAR China), Hungary, Iceland, India, Indonesia, Iran, Iraq, Ireland (Rep.), Israel, Italy, Jamaica, Kazakhstan, Kenya, Korea (Rep.), Kosovo (Rep.), Kuwait, Kyrgyzstan, Latvia, Lebanon, Liberia, Libya, Liechtenstein, Lithuania, Luxembourg, Madagascar, Macao (SAR China), Malaysia, Maldives, Malta, Mauritania, Mauritius, Mexico, Moldova (Rep.), Monaco, Montenegro, Morocco, Namibia, Nepal, Netherlands, New Zealand, Nicaragua, North Macedonia (Rep.), Norway, Oman, Pakistan, Palestinian Territory, Panama, Paraguay, Peru, Philippines, Poland, Portugal, Qatar, Romania, Russian Fed., San Marino, Sao Tome and Principe, Saudi Arabia, Senegal, Serbia, Sierra Leone, Singapore, Slovakia, Slovenia, Somalia, South Africa, Spain, St. Kitts and Nevis, St. Vincent and the Grenadines, Sudan, Suriname, Sweden, Switzerland, Tajikistan, Thailand, Turkey, Uruguay, USA, Ukraine, United Arab Emirates, United Kingdom, Uzbekistan, Vatican City (Holy See), Venezauela or Viet Nam.

That's 147 countries, which means ~50 countries aren't not in this list, e.g. Seychelles, Tanzania or Tuvalu. But getting a visa or a direct flight might not be straightforward.

Update 2021-05-19: Regarding Moo's answer and comments implying that Japan authorities meant to list all countries and simply mistakenly omitted some countries ("I really don't think they put that much thought into it - the list sounds ... odd"), that is incorrect, e.g. read https://www.japantimes.co.jp/news/2021/05/20/national/thailand-travel-ban/ (mirror): it clearly says that some countries such as Sri Lanka and the Seychelles were allowed, until now. One can also see on https://www.iatatravelcentre.com/world.php -> Japan that the list of countries is been updated, e.g. Thailand is currently not on it (but it used to be on it on 2020-08-03, and will but soon be on it again due to Thailand's 3rd COVID-19 wave).