We tend to call this "King James Version Only"-ism. The wikipedia page is reasonably well-written, if you want an overview.

At its heart it's a view of both the textual tradition of Greek and Hebrew texts that undergird the KJV, usually coupled with a view of the process of translation that led to the KJV's translation in the first place.

On the textual side, KJVO advocates usually view the 'Received Text' (Textus Receptus) which underlines the KJV as superior, faithful, and sometimes divinely protected from corruption. They view with disdain and rejection the discipline of modern textual criticism, and tend to favour simple majority of manuscripts, vs. genealogising and 'weighing' manuscripts.

On the process side, some believe that the KJV is an divinely authoritative translation for English and remains so for all time.

The best introduction to this issue is, in my view, the extensive work of Christian Apologist, James White. I suppose you might go around trying to find a secular take on this issue, but quite frankly secular scholars have rarely found the issue interesting enough to do some of the work White has.

There certainly are other translations, a great deal of them. As far as I know, while some argue that particular translations are 'best' on the market, there are not churches functioning in English that have similar views to KJVO in regards to another version.

The KJV of the Bible was the first authorized English translation of the Bible; earlier translators, such as William Tyndale, were hunted down and executed. The translation also has something to do with the idea of allowing more people to more easily read the Bible and come to their own interpretation, rather than relying on the clergy to interpret it for them (though there was backlash against this-primarily from the clergy and others higher up on the social ladder).

For comparison, Gutenberg printed a Latin version of the Bible and the first German version of the Bible came out in 1466. King James, by comparison, didn't ascend to the throne until 1603, so you're talking nearly ~150 years in between. By 1483, for further comparison, there were 9 different German translations of the Bible.

In 1407, Thomas Arundel, the Archbishop of Canterbury, banned English translations of the Bible; six years later in 1413, under the reign of Henry V, English (which had previously been the language used to address social inferiors; French was the language of nobility) became more respectable, particularly after the Battle at Agincourt.

Fast forwarding, the 16th Century's Reformation helped with the push for an English Bible. In Germany, the Reformation under Martin Luther was propelled by religious belief from within (see the 95 theses); in England, by contrast, the Reformation is caused by Henry VIII (notorious for his wives) and is as a result of political and pragmatic reasons, rather than theological ones.

To provide some back information about the English Reformation: around this time period, a strategic alliance between England and Spain is considered very important. In 1525, however, Charles V, the King of Spain, refuses to marry Mary Tudor (Bloody Mary), the daughter of Henry VIII; he has also surrounded Rome, where the Pope, Clementine VII, resides. So, when Henry VIII tries to get divorced from his wife, Catherine of Spain, who is the aunt of Charles V, the Pope refuses.

Makes sense: no reason to let Charles' uncle-by-marriage divorce his aunt and alienate Charles V, who is sieging the city he lives in. So, in retaliation, Henry VIII breaks off and forms the Church of England, but even he is not a fan of an English translation. Thomas More (author of Utopia), for example, is executed for refusing to acknowledge Henry VIII's religious supremacy to the Pope.

Following this, there are a series of translations: Tyndale's, and 1526 edition from Worms that is smuggled into England. Tyndale goes into hiding, then is strangled and burned in 1535. Anne Boleyn, one of Henry VIII's wives who favors an English translation, is executed in 1536, which is a setback. In 1537, Richard Grafton publishes his Matthew Bible: this combines Tyndale's translations with those of Myles Coverdale to complete what Tyndale couldn't. Interestingly, this also includes the Apocryphal books, which are typically not included in most modern day Bibles, so far as I'm aware. (Bel and the Dragon isn't in most editions, for example).

To avoid wading too deep into too much detail, it was proliferation of these frowned-upon Bibles that led to the decision by King James to create an authorized translation to counter these smuggled-in English Bibles, particularly the Geneva Bible, which James was not a fan of.

There are several other versions, however: the Geneva Bible and the Douay-Rheims version are just two translations. Among Protestants, the King James Bible is more popular. The Latin Vulgate Bible is more favored by Catholics, as I understand it.

Backtracking to the beginning for an attempt at a summary that more directly addresses your question: the popularity of the KJV among Protestants has to do with the fact that they made the first publicly, easily available Bible for English-speakers (meant to supplant previous ones, particularly the Geneva Bible, which had begun to get more popular in England prior to the KJV translation), whereas among the more traditional Catholics, the Latin Vulgate Bible is the preferable edition, as I understand it. In addition, the reason it's considered the 'best' version has to do with the attempt at a beautiful, poetic writing style for the writing by the translators.

Source:

Alister McGrath, In The Beginning