Has an individual ever purchased an entire country?

Cecil John Rhodes (1857-1902) wanted to purchase lots of countries he considered 'waste-land' for his Cape to Cairo route in Africa. He even had two of his 'purchases' -- his British South Africa Company (BSAC) was equivalent to anything Leopold of the Belgians attempted -- Northern Rhodesia (Zambia) and Southern Rhodesia (Zimbabwe) named after him. The BSAC ruled both colonial Zimbabwe and colonial Zambia until circa 1924, and continued to influence economic policy in both long after WW2. Rhodes's 'successful' legacy often obscured the basic commercial motives behind his purchases, as did his rather vacuous none sense about 'the British being the finest people . . . so the more of the world they ruled the better'.

From http://kingdomofbiffeche.net/history.htm :

Born in the United States, Edward Schafer (...) an active business man (...) was asked by the Roman Catholic Cardinal of St. Louis to form a committee to aid the needy people of Biffeche.
(...) Edward Schafer put together a group that raised money and sent aid to the people of Biffeche.

A group of Roman Catholic people of the Sérér-Mont-Roland tribe (...) transported to the semi-desert of Biffeche (...). They come from the oldest ethnic group in Sénégal, the Sérér (...)

In 1963 they could not settle upon a new King at the time; instead of choosing one of their own people they asked their priest (...). He advised them to choose the person who had helped them the most during their plight. That person was (...) Edward Charles Schafer.

The United States State Department presented no objections to the new arrangement. The 100th King of Biffeche was enthroned as Edward I by the Grace of God, by the Will of Allah, Protected by the Great White Leopard.

While Mr Schafer's actions did not seem motivated by the obtention of regalian power, and even though Biffeche might not be recognized by all as a separate country ; in the end Edward became King as a consequence of the money he collected and spent for the people of the Land.

The question was seen as interesting enough to get very competent answers, especially referring to the buying of a title of sovereign of a country. But looking closely at its content, I see a lot of ambiguity as to what "owning" and "buying" could mean to the OP. Especially this:

the person who purchased the country, would then be in charge of its governance. However if no such situation exists

So, the OP imagines a case where a country is "bought" (its land, resources, I imagine), but the "buyer" is not in charge. So, the "buying" seems to refer to a very different thing than the buying of a title.

But if the buying of titles counts here, a case that needs to be added to the list is that of the rulers of Wallachia and Moldavia, who in many cases had to or used to give huge bribes to the Ottoman court in order to get the throne of these principalities. Their vassal status involved the obligatory recognition of the princes by the Sultan and even the direct appointment. The Sultan's decision could be directly or indirectly influenced by money incentives, and so the practice became the almost official norm, as a specific part of the Ottoman domination over these countries. It is emblematic of the Phanariot period, but it was already a custom before that, and even a champion of the fight against the Ottoman, like Michael the Brave, bought its way to the throne (for that, it seems that he got even a loan of 200 000 florins from the English ambassador in the Ottoman capital, Edward Barton).

This might not exactly fit the question: Belgian Congo was a personal colony of the Belgian King Leopold II..

From Wikipedia:

After numerous unsuccessful schemes to acquire colonies in Africa and Asia, in 1876 Leopold organized a private holding company disguised as an international scientific and philanthropic association, which he called the International African Society, or the International Association for the Exploration and Civilization of the Congo. In 1878, under the auspices of the holding company, he hired explorer Henry Stanley to explore and establish a colony in the Congo region. Much diplomatic maneuvering among European nations resulted in the Berlin Conference of 1884–1885 regarding African affairs, at which representatives of 14 European countries and the United States recognized Leopold as sovereign of most of the area to which he and Stanley had laid claim. On 5 February 1885, the Congo Free State, an area 76 times larger than Belgium, was established under Leopold II's personal rule and private army, the Force Publique.

In 933 King Rudolph II of Burgundy and King Hugh of Burgundy both wished to rule Italy. So they made a deal. Hugh traded his kingdom of Burgundy to King Rudolph of the other kingdom of Burgundy, thus forming the united kingdom of Burgundy or Arles, in return for Hugh getting the right to rule Italy undisturbed (by Rudolph at least).

So this is an example of a a king trading a kingdom to another king in return for the second king giving up his claim to a third kingdom.

In the Treaty of Utrecht in 1713, the Kingdom of Sardinia and the Kingdom of Sicily were granted to Charles VI, Emperor of the Romans and king of a bunch of kingdoms, and the other kingdom of Sicily was granted to Victor Amadeus II, Duke of Savoy, etc., and titular king of Jerusalem, Cyprus, and Armenia. In 1720 Victor Amadeus II was forced to exchange kingdoms with Emperor Charles VI, who thus had both kingdoms of Sicily, while Victor Amadeus received the kingdom of Sardinia.

So this is an example of monarchs trading kingdoms.

In 1204 the misdirected Fourth Crusade captured Constantinople, capital of the eastern Roman or "Byzantine" empire. The Crusaders selected a dark horse candidate, Count Baldwin of Flanders to be the new Emperor. Margrave Boniface I of Montferrat, the leader of the crusade, was consoled with the title of vassal King of Thessalonika. A number of rump "Byzantine" states were founded, and the three most powerful such states claimed to be the true Roman empires at various times. And two other allegedly Roman rulers got involved in the struggles for power, the Bulgarian Tsar of the Bulgarians and the Romans and the Turkish Sultan of Rum (Rome).

Thessalonika was gradually conquered by Epirus, the city being captured in 1224. Boniface's son King Demetrius died childless in 1230, and left his claim to the Kingdom to Holy Roman Emperor Frederick II in his will in 1230. Emperor Frederick granted the claim to Thessalonika to Margrave Boniface II of Montferrat, half nephew of King Demetrius, in 1239.

Constantinople was recaptured by the "Byzantines" in 1261 and Emperor Baldwin II fled. Various popes tried to arrange a new crusade to put the Latin Emperor back on the throne, and "Byzantine" Emperor Andronikos II Palaiologos tried to arrange a marriage of his heir Michael IX with Empress Catherine I, heiress of the Latin Empire, in order to avoid the danger of a crusade. He failed, but did marry as his second wife Yolanda of Montferrat in 1284, who brought her family's claim to the Kingdom of Thessalonika with her, and a son of theirs became Margrave of Montferrat when Yolanda's brother died in 1305.

Latin Emperor Baldwin II lost his capital and the lands he directly ruled in 1261, and his remaining vassals apparently didn't pay him much tribute, so he was short of money. And an attempt to reconquer his lands would be very expensive.

So in 1266 Baldwin II sold the right to the Kingdom of Thessalonika to Hugh IV, Duke of Burgundy, even though Margrave William VII of Montferrat already had the rights to the Kingdom of Thessalonika.

Then in 1274 Emperor Philip of Courtenay, son of Baldwin II, granted the rights to the Kingdom of Thessalonika to Philip of Sicily (1255/56-1277), even though Margrave William VII of Montferrat and Duke Robert II of Burgundy already had claims to the Kingdom of Thessalonika.

Philip of Sicily's claim died with him in 1277, William VII's was given to his daughter Yolanda when she married Emperor Andronikos II in 1284, And Duke Odo IV of Burgundy sold his rights to the Kingdom of Thessalonika and the Principality of Achaea to Count Louis of Cleremont, first Duke of Bourbon, in 1320.

And I suppose that it is possible that rights to the Kingdom of Thessalonika were sold to someone else at some time.

IN 1453 the Ottoman Turks conquered Constantinople and the last "Byzantine" Emperor Constantine XI was killed fighting. In 1460 the Ottomans conquered the Morea and Constantine XI's brother Despot Demetrius Palaiologos (c. 1407-1470) submitted to the Sultan. His only known child Helena entered the harem of the Sultan and died in 1469, and Demetrios became a monk before he died.

Despot Thomas Palaiologos (1409-1465), the youngest brother of Constantine XI, fled to western Europe, and was recognized as the claimant to the "Byzantine" Empire. Thomas's younger son Manuel Palaiologos (1455-1512) lived in Italy for much of his life and then traveled to Constantinople to the court of the Sultan. He sold his rights to the empire to the sultan in return for an estate and a pension. He had a son John who died young, and a son Andrew who converted to Islam.

Andreas Palaiologos (1453-1502), the older son of titular emperor Thomas, succeeded as titular emperor. He sold his rights to the "Byzantine" empire twice, to King Charles VII of France in 1494 and again to King Ferdinand and queen Isabella of Aragon and Castile.

In 1846, The East India Company annexed the Kashmir Valley, Jammu, Ladakh, and Gilgit-Baltistan from the Sikhs, and then transferred it to Raja Gulab Singh of Jammu in return for an indemnity payment of 7.5 Million (Nanakshahee) Rupees, making it an interesting incident in the history when a private company (annexed and) sold a state. [1][2]

In certain sense yes. Didius Julianus purchased the position of the Roman emperor in 193. This position was actually auctioned by Praetorian guards to the highest bidder, the Wikipedia article on Didius Julianus contains a short account. The story is described in detail by Dio Cassius, in his Roman history, book 74, 11-17.

The American movie "Fall of the Roman empire" (1964) shows a fictionalized version of these events.

Of course one can argue in what sense a Roman emperor "owned" the country. At that time the emperors were absolute rulers, but not to such extent as later Chinese or Moscow emperors.

Remark. The title of the movie is misleading: the Empire was still very far from its fall. And in general, the movie has nothing to do with history, except using some historic names.