I worked on something like this in the Home Office about 5 years ago (visas-immigration.service.gov.uk). We had 3 lists:
The first is straight forward enough, but you still have to decide whether places like Gibraltar are listed separately - they are countries, but not sovereign states. Then there is the minefield of states that the UK doesn't recognise - e.g. Taiwan.
The second is different, and mostly on a par with sovereign states, but, for example, the UK has several forms of citizenship. e.g. (from the aforementioned service):
The third is for questions such as Country of Birth, where countries that no longer exist are still legitimate answers.
on the passports service- what is the correct answer to the question "Nationality at time of birth", if the country no longer exists - in the case of Former Yugoslavia for example? It would be good to have some guidance around this question on the passport application form.
I would recommend the question should be "Country of birth" rather than nationality as nationality can be more complex. For instance, I was born in the UK, but "British Citizenship" didn't exist when I was born, I was a "British Subject and Citizen of the United Kingdom and Colonies". Asking country is less of a minefield.
I would also suggest you look at the visa service I mentioned above. This asks this very question and allows users to enter extinct countries, such as Yugoslavia.
I'd be cautious about asking for country of brith if what is wanted is a person's nationality, or first nationality. Being born in a country does not necessarily imply someone gains the nationality of that country (though often it is the case).
NB: I'd be curious why a service needs nationality at time of birth rather than current nationality or nationalities. Which would obviously avoid the issue of countries that have ceased to exist (though presumably their nationalities have been subsumed / are known to translate to a currently recognised nationality).