Baptistest

Mississippi has a lot of Baptists - 55% of the population, making it the most Baptist state in the US.  However, it's only the second most Baptist state in the world.  First place goes to an isolated mountainous state in the very far Northeast of India called Nagaland, where a solid 75% of the population is Baptist.

For centuries, its difficult terrain and obscure location kept Nagaland and its indigenous tribes largely uncontacted, except for brief, often hostile encounters with neighboring groups.  This meant that ancient customs and religious practices persisted undisturbed by upheavals in the rest of India such as the arrival of Islam or European colonization.  When the British finally sought to establish control over the area in the mid 1800s, they found a region described as "headhunters' paradise" (anyone other than the British would've found someone else to conquer upon hearing that description), and had to fight against decades of guerrilla resistance from the local tribes.

When Baptist missionaries arrived in 1870, they found that the area's isolation meant that there was little competition from other major religions for converts.  The traditional animist religions were replaced by Christianity over the next hundred years, and headhunting was eliminated (apparently "Headhunters for Jesus" didn't catch on).

Nagaland's history of isolation and cultural differences with the rest of the subcontinent meant that they felt little reason to join India in the 1950s, aside from the fact that the British told them they had to (as is so often the case throughout history).  A nationalist insurgency has been simmering in the region ever since, with a fragile ceasefire holding back open war between the Indian military and Maoist rebels.

Trapezium Nullis

If you want to start your own country, it's tough to find any land to lay claim to.  The entire map is painted one color or another, so unless you want to try your luck in the frigid wastes of Marie Byrd Land in Antarctica, or look for an abandoned ocean platform like Sealand, the prospects look pretty grim.

However, thanks to the wonders of international politics and border disputes, there is one patch of land that no one seems to want.  As with all border issues, the problem can be traced back to the British.   At the end of the 19th century, the British had control over the area, and they decided that the border between the region administered from Cairo and the region administered from Khartoum should be a straight line.  Any third world country which has a straight-line border drawn by a British cartographer has probably run into issues with it, and in this case the British themselves found a problem.  There's a triangle of land along the coast of the Red Sea which is closer to Khartoum and to Cairo, but was North of their line.

So, 3 years later, they drew a new line, this one dipped a bit below the old line, and then rose back above it to place that triangle under Khartoum's authority.  The area in that little dip is called the Bir Tawil Triangle (despite being roughly a trapezoid).  Fast forward to today, and both countries want the valuable Red Sea coast line, and couldn't care less about Bir Tawil.  Egypt claims the original straight line border, which places the coast line on their side, and gives Bir Tawil to Sudan, while Sudan claims the revised border, which does the opposite.  Both sides vehemently insist that Bir Tawil does not belong to them (as accepting it would mean ceding the much more valuable territory), and it is therefore essentially the last unclaimed habitable territory in the world.

An Army of One

If there's one thing the British Empire was good at, it was invading countries - and they had lots of practice.  In fact, the significant majority of the world has been invaded by British forces at some point or another, with only a few scattered areas including the Marshall Islands, Monaco, Burundi and Paraguay remaining before Britain collects them all.

In the late 1830's, Britain was worried that the new ruler of Afghanistan might be getting a bit too friendly with the Russian Empire and decided to fix it.  By invading, of course.  Initially, things went quite well.  Dost Mohammad Khan was deposed and exiled to India, the old, pro-British ruler Shah Shujah was restored, and the British set up camp just outside Kabul.  Although the area seemed peaceful on the surface, the son of the former ruler, Akbar Khan, was out gathering support from the rural tribes, who preferred his father to Shah Shujah.

In 1842, things turned ugly.  The low-level guerrilla warfare in the distant areas transformed into open revolt in Kabul.  In early November, an angry mob stormed the residence of one of the British officers, and murdered him and his staff.  A few days later, they looted a supply fort.  The man in charge of British forces in the area, Sir William Elphinstone, took little action, apparently hoping this would all blow over.

It didn't.  By late November, the Afghans had set up gun positions on the hill above the British position and began bombardment.  With winter closing in, and no reinforcements on the way, the British soon realized they would have to negotiate a safe retreat.  Akbar Khan, using the Brits' greatest weakness against them, invited some of the officers to tea to discuss a peaceful solution.  As soon as they stepped off their horses, the British delegation was killed.

Elphinstone, again, decided to let that slide.  In early January, he agreed to Akbar Khan's terms of surrendering the British gunpowder and many of their weapons in exchange for a guarantee of safe passage.   As one might expect given the story thus far, as soon as the 16,500 troops and other personnel got on their way, the Afghans opened fire and pursued.  Akbar Khan was still rather angry about the whole "invaded and deposed by father" situation, it turned out.

The next day, Elphinstone met with Akbar Khan again, who explained that the British had left sooner than expected, and he had not had time to negotiate their safe passage with the tribesmen.  Elphinstone, being the most gullible man in history, agreed to wait.  Again, they were betrayed, and Akbar used the time to set up additional ambushes in the mountain passes ahead.  Akbar Khan was not only still angry, but also a bit of a jerk.

By the fourth day, well over 3,000 people had been killed.  As the journey continued, many attempted to turn back under promises of protection from Akbar.  I'm sure we can all guess how that turned out.  Ultimately, out of the 16,500 people who set out from Kabul, only a single man, William Brydon made it back to Jalalabad.  When asked where the army was, he is reported to have replied, "I am the army".  In any other context, that answer would have been incredibly badass.