To begin with, there is a very good article on Wikipedia about this hymn which appears to be thoroughly researched and referenced. Especially interesting is the media clip of an old version of the song being "lined out," that is, the group would pause to allow the leader to sing a verse or so ahead to remind the group of the words coming up: an essential technique in an age when many groups wouldn't have the resources to purchase hardcopies of numerous hymnals--if any were even available. Also of interest there is the graphic of an 1847 shape-note version when only four shapes were used (Fa, So, La and Ti--the older solfege system) in three-part harmony. The article also includes all six stanzas of John Newton's original poem.
Click on all graphics to enlarge.
The oldest version of the song that I have in my collection is shown above, from the 1897 book Songs for Young People. This version, unlike the most common known to many of us, is not set to the "New Britain" tune but to original music by F.S. Shepard, who used stanzas 1, 2, 3 and 5 of the original poem and added his own chorus, writing the song in 4/4 time (the "New Britain" version is in 3/4).
The next version, above, is the standard "New Britain" tune with harmony arranged by E.O. Excell, who used stanzas 1, 2, and 3 of the original poem with the final verse that is now considered the traditional final verse but is not original. It was actually written by Harriet Beecher Stowe for her book Uncle Tom's Cabin (1852). This version is from the 1917 hymnal Treasury of Song.
The third version, from Gospel Melodies of 1928, is the E.O. Excell arrangement once again, except in a more easily readable version and with an "amen" cadence added to the end.
Next we jump up to 1961 with a version from Songs of the Church. This is also obviously the E.O. Excell arrangement, and is the longest version I've seen, with six stanzas. Stanzas 1 through 5 are from the original poem, with the final stanza being Stowe's "ten thousand years" instead of the original. We also now see it for the first time (as far as my own collection goes) written in the familiar 7-shape system commonly used by the Church of Christ. The final "amen" cadence has also been dropped since it is not generally the custom of congregations of the Church of Christ to sing an amen at the end of a hymn--the "amen" traditionally being reserved for prayers only. Personally I don't see any scriptural problem with singing an affirmative "amen" at the end of a song, but that's just me.
The version above is from The Mennonite Hymnal of 1969. The harmonic arrangement, according to the details you can see just above the staff on the top right, is from a collection much older than E.O. Excell but is similar to his harmony. This version uses only the first four stanzas of the original poem. According to the introduction to this book, the Mennonites went to great lengths to preserve old hymns such as this in their original state, or as close as they could get to it, so it doesn't surprise me that this version doesn't include Stowe's "ten thousand years."
This version, from Sacred Selections for the Church from 1974, is notable for a new name among the arrangers and a different arrangement, though it doesn't look all that different at first glance. With music by William Walker, it introduces a minor VI chord in the third full measure which adds some nice color in my opinion. Another difference in harmony is the ending chord, in which he uses a full tonic (Do-Mi-So-Do) rather than dropping the So and tripling the Do like Excell did. Either way is perfectly fine, but the full Do-Mi-So adds an extra richness (again, in my opinion). Here we have the first four stanzas of the original poem plus Stowe's now ubiquitous final stanza.
This version is from Songs of the Church of 1977. Although not credited, here we see once again Walker's harmony, though slightly rearranged. This is also the first time in any of my books that we see the four-stanza version most of us are familiar with: the first three stanzas of the original poem plus Stowe's final stanza. The final chord differs in that the alto and tenor parts are switched with each other; consequently the harmony leading up to that chord is also a little different although the same chords are used.
Another variation in harmony can be seen in the above, from Hymns of Praise from 1978. Although we are not told who the arranger is, this style of harmony looks very familiar to me and I would not be surprised if I was told that it was arranged by Holland Boring, Sr. He was one of the compilers of this hymnal and a prolific songwriter himself (and the man who taught me harmony). The third measure, rather than using the tonic chord (Do-Mi-So) of the older versions or Walker's minor (La-Do-Mi) chord, uses a major IV chord. The accidental on the last note of the previous measure causes the progression to "slide" naturally into that IV chord. Another accidental, on the last note of the sixth measure, creates a temporary modulation, or key change, into the following measure. The song then returns to the original key in the measure after that. This is the "short version," using only the first two stanzas of the original poem plus Stowe's final stanza.
This version is from about 1983 in the book Gleam of Glory. I include it here for completeness; it uses the original first three stanzas plus Stowe's final stanza, set to entirely new music by Boring in 4/4 time.
I have several more books with various versions that are identical to various of those above, so I will not bother noting them individually here. However, there is one more version that is the most modern I know of and which I don't particularly care for.
What a mess. This is a perfect example of how to destroy a classic, well-loved hymn. Who is really going to try to sing all that? And what is up with all those descants? And 9/8 time? Really? For nearly 200 years people were happily singing this song, but Alton Howard decided it needed to be "improved" or something. This looks like it was written for a professional choir and not for a congregation who mostly (almost entirely) cannot read music and wouldn't know what to do with this mess anyway. This is why, when I lead this song, I tell everyone to ignore all that stuff and just "sing it the way you remember it." There are also some harmony mistakes in here that I would never have been allowed to get away with when I was being taught, but I'm not going to bother detailing them.
"Amazing Grace" is written in 18.104.22.168. meter. That means 8 syllables in the first verse, 6 in the second, and so on. There are many songs written in this meter, which means the words to any one of them can be sung to the music of another. So if a group wants to sing one of them, say, because it deals more specifically with the sermon of the day, but that group doesn't know the music, they can just sing the new words to the tune of another song that they are familiar with. Although the "New Britian" tune is the most popular for "Amazing Grace," the words have been used with music from other 22.214.171.124. songs. One that I realized myself one day, although I don't know what led to this realization, is that the words to "Amazing Grace" can be sung perfectly well to the music of Hank Williams' "I'm So Lonesome I Could Cry." Try it sometime.
None of the versions I've recounted above used John Newton's final stanza from his original poem, so I thought a good way to end this post would be to reprint it here.
The earth shall soon dissolve like snow,
The sun forbear to shine;
But God, who called me here below,
Will be forever mine.