Almost all developed countries and many developing countries have systems of public schools, though the specifics of funding, governance, and curriculum vary widely. There's no country that *doesn't* offer some form of publicly funded education, although the extent of that funding and the accessibility of the system may differ drastically.
Instead of listing every country, it's more accurate to say that the absence of a public school system is extremely rare. Countries might have a mix of public and private schools, with varying degrees of government oversight and support for each.