Maybe my history with church is limited here in the United States, but I feel as though most denominations in which singing is encouraged follow a similar tune when singing various hymns. I'm not sure if this is the case in other English speaking countries, though I do know some Spanish churches also have similar tunes. Do churches that sing in other languages share any relationship to the English speaking melodies?
I'm just wondering how this element of organized religion got, well, organized.
It depends on the hymn, but some of the melodies for hymns are very old indeed, dating from late antiquity or the early Middle Ages. These oldest tunes were the standard accompaniments to the Roman Catholic liturgy. Psalmodies, the tunes to which the psalms are sung between the liturgical readings, are some of the oldest and most constantly used
So, yes, while words change there is a huge reuse of melody within liturgical music, much of it pointing back to these traditional forms or modifications thereof.
Church music and words are sometimes written to go together (sometimes even by the same person), but in other cases the words are used with several different tunes. A tool for interchanging hymn tunes is called the “meter”. Just like in poetry, it refers to the number of syllables in a line. You’ll usually find it in a hymnal next to the tune name or composer’s name, either under the title or at the bottom of the page. Any two hymns (words) with the same meter can usually be sung to the same piece of music. The back of the hymnal has a “metrical index” which will list the tunes according to meter. For instance, 8.6.8.6 refers to a song with 8 syllables in the first line, six in the second, and so forth. “Double” means the meter repeats in the tune (so two verses become one verse). Here's a more in-depth description.
So, for example, you can take the words to “Joyful, Joyful, We Adore Thee”, generally sung to “Ode to Joy” and sing them instead to “Erie”, to which tune is commonly sung “What a Friend We Have in Jesus”. They are both 8.7.8.7.D meter. It’s fun to mess with your church friends this way.
American Protestant worship has a long history of hymns and congregational singing. Originally, only psalms were translated and set to music. Over the centuries, many famous writers have written hymns and composers have written hymn tunes. There are several “streams” of origin of American hymns: European establishment church music (like Bach chorales); non-conformist hymns ( Isaac Watts, the Wesleys, the Welsh hymns); American shape note tunes, which started as singing schools; the evangelical music of the third Great Awakening in the nineteenth century; the African-American spiritual tradition; and twentieth century writers/composers worldwide. Missionaries sometimes used the familiar tunes with words in local languages; there is also plenty of original music in the non-English-speaking Christian world.
Church-goers become very emotionally attached to their music, as they have learned it. In the mid 1800’s, a couple of English clergymen set out to compile a collection of hymns to standardize them. This collection is called “Hymns Ancient and Modern”. It set the tradition for new hymnals to be despised by their users for “changing” hymns—it has sometimes been referred to as “Hymns Asked for and Mutilated”. Most of the large denominations publish their own hymnals (often with worship resources included), and there are also independent hymnal publishers like Hope Publishing.
Enthusiasts may consider the Hymn Society for further edification.