What country has no daylight?

All countries experience, at least in some regions, the absence of the sun. So, no country never gets dark.

Nevertheless, areas near the Arctic and Antarctic circles - the extreme norths and souths of the globe - can endure long periods of light and dark. The links below outline how this works.

Your best bets for countries with little darkness would be those very close to or bordering the Arctic/Antarctic Circles. These are: USA (Alaska), Canada, Denmark (Greenland), Iceland, Norway, Sweden, Finland, Russia or any country with claims of Antarctica.