Today let's take a look at the Japanese versions of "Hark! the herald angels sing." This has been translated a few times; Wikisource has a convenient collection.

Before we get started, let's look at our base text for comparison: the standard contemporary version, by Charles Wesley, George Whitfield, and Martin Madan. (Sequentially — see Tim Phillips's summary of the history of the piece for more on this.)

Hark! the herald angels sing: "Glory to the new born King!
Peace on earth, and mercy mild, God and sinners reconciled!"
Joyful, all ye nations rise, join the triumph of the skies;
With th' angelic host proclaim, "Christ is born in Bethlehem!"
Hark! the herald angels sing: "Glory to the new born King!"

So the first translation at Wikisource is from the 1891 Seikōkai sanbika 聖公会讃美歌 ("Hymns of the Anglican Church"). I've included a back-translation that's as close to word-for-word as seemed reasonable.

1891 Japanese translation of "Hark! the herald angels sing"

"Kami ni wa sakae, chi ni wa odayaka,
Yohito to kami to yawaragitari!" to
Mitsukaitachi no utaeru uta o
Hitobito kikite tomo ni yorokobi
Kyō aremaseru kimi o homu beshi

"Glory to God, peace on earth;
The people of the world and God are reconciled!":
Such is the song the angels [messengers] sing;
Let the people hear it, rejoice together
And praise the Lord who is born today.

Quite close to the original, especially that use of yawaragitari (about which I hope to post more sometime soon).

Next up we have a version from Sanbika 讃美歌 ("Hymns"), published in 1903 by the Christian Literature Society of Japan (教文館). I'm only going to give the first two lines from now on.

1903 Japanese translation of "Hark! the herald angels sing"

"Kami ni wa sakae, chi ni wa odayaka
Hito ni wa megumi are!" to utaeru...

"To God, glory; to earth, peace;
To people, mercy let there be!" they sing...

This one departs from Wesley's phrasing and goes straight to the source, i.e. Luke 2:14. In the most recent translation that would have been available at the time (the 1887 "Meiji Version" 明治元訳), the phrasing is very similar:

Luke 2:14, 1887 Meiji Version

天上（いとたかき）ところには栄光（えいくわう）神にあれ　地には平安（たいらか）　人には恩沢（めぐみ）あれ

Ito takaki tokoro ni wa eikō, kami ni are; chi ni wa tairaka, hito ni wa megumi are.

In the highest place, glory to God let there be; on earth, peace; towards people, mercy let there be.

My paraphrase is especially stilted to preserve the order; the KJV version is more familiar:

Or as the KVJ has it:

Luke 2:14, King James Version

Glory to God in the highest, and on earth peace, good will toward men.

However, as any fule (or Latinist) know, this is a mistranslation. The 1917 Taisho Revised Bible (大正改訳聖書) addresses this issue, and has the verse as follows:

Luke 2:14, 1917 Taisho Revised Bible Version

いと高き處には榮光、神にあれ。地には平和、主の悦び給ふ人にあれ

Ito takaki tokoro ni wa eikō, kami ni are; chi ni wa heiwa, kami no yorokobitamau hito ni are.

In the highest place, glory to God let there be; on earth, peace towards the people in whom God rejoices let there be.

Which is much more like, say, a more contemporary English translation of the verse:

Luke 2:14, New International Version

Glory to God in the highest heaven, and on earth peace to those on whom his favor rests.

Presumably as a result of this change, the Hymnal Committee (讃美歌委員会)'s 1931 Sanbika 讃美歌 ("Hymns") contains a suitably updated version of the hymn too, and that is the (a?) version that is still sung today:

1931 translation of "Hark! the herald angels sing"

"Ame ni wa sakae, mikami ni are ya;
Tsuchi ni wa yasuki, hito ni are ya!" to...

"In Heaven, glory to God let there be;
"On Earth, peace to people let there be!" ...

Note that the hymn translators carefully left out the "on whom his favor rests" part. Might have been purely metric, might have been political (minority religion, etc.), but I like to think it was because they just recognized that pedantically circumscribing the peace proclaimed by the angels would make for a sucky hymn.