This is a common trope in sci fi, where people live on land that's owned by a large corporation. Depending on where the work falls on the dystopia/utopia spectrum, most of the things on the land might be controlled by the corporation and they probably have a private military at least, with private police branches that enforce rules and such.
Has such a thing happened in real life? I'm under the impression that companies like United Fruit, Standard Fruit and the East India Trading Company exhibited certain signs of this but weren't really "governing" in the modern sense of a government. Am I wrong about this? If I'm not are there places where this actually happened?
This is an interesting question and right up my (very narrow) alley. My research area is the very early development of private corporations. Unfortunately I can't help you with more recent examples that you might be looking for, like United Fruit.
However, I can point you toward toward the earliest example I have found of a "private" for-profit, joint stock, dividend-bearing corporation, the Mahona of Chios. The Mahona (a word that might come from the Greek meaning “a share, a unit”, or from Arabic meaning “a financial contribution”) literally governed the island of Chios, a Greek island, along with its trade and some nearby islands, from 1346 to 1566. It was a Genoese institution, and ruled under Genoese law, but the affairs of the Mahona and the island were run by the administrators of the Mahona. Interestingly, the island itself was under the sovereignty of the Byzantine empire (and later, the Ottoman empire), but the Mahona maintained control of the island by paying tribute to the Byzantines and then the Ottomans. So, despite this being a very old example, it fits the model that you seem to be expecting (in your United Fruit example) - a foreign corporation functionally governing some territory while paying off the proper government.
Chios was a valuable island to control, as it was the almost exclusive producer of mastic, a plant resin that can be used as chewing gum or for industrial purposes. The Mahona was profitable, returning regular dividends to shareholders over its 200 year existence. It ended when the island was conquered by the Ottomans.
The origins of the Mahona make an interesting story. The Mahona was set up by a group of rich Genoese citizens, each of whom purchased and supplied a war galley in an ongoing war against some exiled nobles living in Monaco. The citizens' investments were guaranteed by the Genoese government - this was basically a way for Genoa to quickly raise war money without directly taxing its citizens. The exiled nobles then fled Monaco, and the war fleet then decided - and this is such a jump that I have a hard time understanding it - to instead invade Chios, which was formerly a Genoese possession but then under the control of the Byzantines. The island was conquered, its local nobles subdued, and the Mahona leaders sailed back to Genoa to negotiate with the Genoese government. The Mahona wanted to get paid back for the expense of the war fleet plus their conquered prize- basically, they wanted to sell Chios to the Genoese government.
Instead, the government made a deal - Genoa received sovereignty over the island, and ownership of the towns and forts. The Mahona received usage-rights of the island and all profits. Genoa reserved the right to buy shares in the Mahona, with the idea that eventually Genoa would have the money to buy the whole thing. It never happened - the government wasn't ever able to afford the shares. Later, new deals were struck, altering the corporate governance of the Mahona, but Genoa was never able to purchase the island from the Mahona outright.
Mahonas were also set up for other islands in the Mediterranean, but I have much less information on those.
There are a couple of interesting lessons or tensions in all of this. First, is a corporation really "private", when it functionally governs a territory? Is it an extension of it's home government, or the private territory of the shareholders? Second, the "technology" of corporate governance (that is, how a corporation is run under the laws of a higher government, but with its own powers over property and even people) has a long, long history. Third, colonization (Chios was a colony of Genoa!) existed well before the New World, and the model used by Genoa was a forerunner of those used by England/Britain - which often "chartered" colonies paid for by rich people.
If anyone has more information or sources for Genoese Mahona or other early corporations, please share!
Sources: P.H. Argenti, The Mahona of the Giustiniani: Genoese Colonialism and the Genoese Relationship with Chios, in 6 Byzantinische Forschungen 1 (Adolf M. Hakkert & Peter Wirth eds., 1979)
William Miller, The Genoese in Chios, 1346-1566, 30 Eng. Hist. Rev. 418 (1915)
Ferrarini, Origins of Limited Liability Companies, in VOC 1602-2002: 400 Years of Company Law (Gepken-jager et al eds., 2005)