Most countries, except for some island nations, have boundaries that have been arbitrarily drawn in times of empire. Many don't make sense, and many cut across natural geographic or ethnic lines that would easily suggest themselves. Others however are downright bizarre, and some of the most glaring oddities are the following.
France
How far is Canada from France? 7,000 miles, 5000, miles or 10,000 miles?
Well none of the above is correct. France and Canada are in fact only 17 miles apart, and that's official. A mere 17 miles south of Newfoundland lie a group of islands collectively known as St Pierre et Miquelon, and they don't just belong to France, they are France.
The French first got there centuries ago, and since then there has been a bit of a chequered history with tempers flaring between France, USA, Britain and Canada. When the dust settled these little dots in the ocean were flying the French flag as they do to this day.

Although Canada is next door, the inhabitants of St Pierre et Miquelon send a deputy not to Ottawa, but to the Assemblée Nationale (Parliament) in Paris, and one to the French upper house. Letters to and from the islands from mainland France are treated as domestic mail, and charged at the domestic rate. The currency of France, the Euro, is the currency of the islands and the Head of State is Nicholas Sarkozy, the President of France.
During the 1930s the islands became important in the liquor smuggling trade to the USA with the advent of prohibition, but it was the rich fishing stocks in the area that the economy has always relied on. In these days of reduced fish numbers the French government are trying to diversify, particularly into tourism.
And St Pierre et Miquelon aren't France's only contribution to the fascinating world of geopolitical farce. French Guyana in South America is not really a country; it is a départment of France, again sending elected representatives to Paris. Like the islands it uses French currency, and enjoys Nicholas Sarkozy as Head of State, and in several referendums the people have overwhelmingly voted to stay with France. The Caribbean islands of Martinique and Guadeloupe fall into the same category.
Azerbaijan
Poor little Azerbaijan. Not many can find it on the map, not many can spell its name correctly, and not many care. Part of the USSR for decades, it emerged as a nation state on the 1990s only to be plunged into bloody battles along ethnic lines. A large Armenian population wasn't so happy, and Armenia drives a physical wedge through the small nation cutting off an even smaller exclave called Nakchivan from the main territory.

But Azerbaijan has oil, so some have learnt how to spell its name, some have sought it out on the map, but few still care about it apart from the petrodollars that can be earned from it. A pipeline links the oil reserves in deep water fields in the Caspian Sea to the Turkish Mediterranean port of Ceyhan, giving the West access to huge quantities of oil and gas. Russia's not best pleased.
Nakchivan, although an integral entity of Azerbaijan, has an autonomous government, but remains geographically isolated from the rest of the country and more or less from the rest of the world.
Cabinda
The southern African country of Angola throws up our next strange border arrangement. On the Atlantic coast and to the north of the country, the province of Cabinda has become estranged from the mother ship, with a finger of the Democratic Republic of Congo (Congo Kinshasa or Zaire to those of a certain age) insinuating itself towards the sea.

The other Congo (Brazzaville) lies to the north, and there seems to be a continued struggle by those who live in the province to achieve independence. Attempts to declare the Republic of Cabinda have met with failure but you can't fault people for trying.
Lesotho
We stay in southern Africa for this next peculiarity as we focus in on the world's only sovereign state to be completely surrounded by one other state, namely South Africa. But how much sovereignty or independence can a country have when it finds itself having to tow the line to guarantee trade links with the outside world?

Another of Lesotho's claims to fame is that it is the only independent state to lie more than 1000 metres above sea level in its entirety, and there can be sufficient snow on the higher mountains to attract skiers from South Africa!
The political history is a mess of coups and intrigues and the Kingdom is now described as a constitutional monarchy with a king as figurehead.
Kaliningrad
And so to northern Europe. Kaliningrad is an integral part of Russia, cut off from the huge bulk of the rest of the country by Poland and Lithuania. Russia was (is) especially keen to hold onto this little bit of land because it offers a port on the Baltic, indeed the only port on the Baltic that remains ice-free all year round, a handy place to park your fleet of war ships.

Things went Moscow's way without a hitch when it controlled the Baltic states, but with the break-up of the USSR Kaliningrad became isolated. Now travellers, civilian and military, have to pass through NATO territory if they wish to get from Kaliningrad to the rest of Russia by land, and special travel arrangements have to be made for locals.
It used to be a Prussian town, did Kaliningrad, and there are moves to restore its pre-Soviet name of Kőnigsberg. One of its claims to fame is that Immanuel Kant was born there, though pure reason would suggest that there might be more to the city than that. It was hoped that Kaliningrad would become the “Hong Kong of the Baltic” for Russia, but crime and corruption have deterred trade and investment so it remains very much a dark, isolated oblast some 200 miles from Russia proper.
Others???
Well there are others a-plenty. Spain enjoys sovereign sway over the cities of Ceuta and Melilla which sit on Moroccan soil, and Britain owns Gibraltar in Spain, but perhaps the strangest of all this geopolitical nonsense is the United Kingdom of Great Britain and Northern Ireland. Why would one island own half of a neighbouring island as well? Why would people as sane and sensible as the British want to govern the Irish? Why indeed?