There is no Atlantic Circle.
The Antarctic Circle passes through no countries. See the related link for a map of the Antarctic Circle.
None.
The Antarctic Circle passes through Antarctica, which is a continent with no countries.
None.
None.
None.
None.
None. Any land that the Antarctic Circle crosses is part of the continent of Antarctica, which is not carved up into countries.
None. No states or countries either.
None. The only land that the Antarctic Circle crosses is on the continent of Antarctica. There are no cities, states, provinces, or countries on that continent.
The land on the Arctic Circle is divided among eight countries: Norway, Sweden, Finland, Russia, the United States (Alaska), Canada, Denmark (Greenland), and Iceland (where it passes through the small offshore island of Grímsey).
None. There are no countries, cities, or permanent human residents on Antarctica, and that's the only continent the Antarctic Circle crosses.
None. The only landmass it passes through is Antarctica, which contains no countries, mainly just science stations run by countries like Britain, Chile, Australia and Argentina. If you are also including the Arctic Circle in this question, the Arctic Circle passes through: Russia, Finland, Sweden, Norway, Iceland (the island of Grimsey), Greenland (which is still sort of technically part of Denmark), Canada, and the United States. So it passes through eight countries.