In the eighties, there were two different Norwegian translations of Garfield: one in which he kept his original name, and one in which he was named Pusur. The former tried to stay close to the original text, while the latter sometimes altered the text completely, changing the content of entire storylines (a sequence where Jon and Garfield are watching a horror movie is changed to having them watch a crappy vaudeville show, complete with references to Norwegian celebrities). Sometimes the translators were even adding political commentary. Eventually, the fomer school of translation won out, but the name Pusur remained and became canon.
In The Pre-History of The Far Side, Gary Larsen discusses a change that was made in one of his cartoons before it was distributed to foreign markets. In the cartoon, a ship drops a microphone into the water to record whale songs, and a whale swims up to the microphone and sings "Louie Louie". In some foreign markets, the whale instead sings "Singing in the Rain". Larsen admits that Singing in the Rain was funny, and writes that the song change was probably due to Louie Louie being less well-known outside of the US.
In another, he mentions one of his cartoons (a penguin indistinguishable from the others sing "I gotta be me") turned into a greeting card, with the difference that the singing penguin was turned yellow. He regarded this as an inversion for Completely Missing the Point of the cartoon.
In one strip, Calvin complains about "the lack of sex education" because the English language doesn't have grammatical genders. When it was translated into Norwegian, which does have grammatical genders, "Tommy" instead complains about grammatical genders being politically incorrect.
This can result in a pun which cannot easily be retranslated back to English. The card Lightmine Field was translated into Italian as Campo Illu-Minato - "illuminato" meaning "illuminated" and "minato" meaning "mined" in the sense of having explosives placed in it.
The Slivers - Hive Mind creatures, each of which grants abilities to all the others - are known in Italian as "Tramutanti", from the same root as English "transmute".
What may be the most amazing translated name, the Yu-Gi-Oh! card called "Mind Hack" in Japanese was astonishingly renamed Mind Haxorz in the English translation.
Other cards that had "death" in the name were translated as "Des," for cards such as "Des Koala" and "Des Frog." Initially just a Bowlderization. Then comes "D.3.S. Frog" (a fusion of three Des Frogs).
The French translation of the ork tellyporta from Warhammer 40,000 is "téla-tépula", which means "you iz here-you izn't here no more". An orkier description of a teleporter you will not find.
Brian Hooker's excellent translation of Cyrano de Bergerac. He substituted lines and allusions to William Shakespeare and Marlowe which were appropriate to the classical French theatre quoted in the original text. This inspired Anthony Burgess to use the same approach in his own translation 50 years later.
The Metropolitan Opera adaptation of Die Fledermaus by Howard Dietz and Garson Kanin is usually not a literal translation but fairly close; it gives actual lyrics to the refrain of the waltz ensemble whose original German text is "duidu, duidu, la la la la la." Sometimes, however, they couldn't be bothered to do anything more literate than a Better than a Bare Bulb spoof, as in the Irrelevant Act Opener which now ran, "It's the kind of libretto where we all are at a ball."
The English version of Les Misérables. "At the end of the day", for example, takes all the best from "Quand un jour est passé", gets rid of the less effective lines and most importantly is easier to sing. The original lyrics are impossibly hard to articulate clearly; the translation is more musical because of the added alliterations, etc.
Bakura is changed from British to Scanian, with appropriate cultural references changed (like eating spettekaka instead of bangers and mash). Likewise, Joey is from Stureplan instead of Brooklyn.
As the final Harry Potter book had been out for years when the Swedish dub of episode 23 was released, the book Téa had spoiled was changed to the final Twilight book, and her ship is changed from Harry/Hedwig to Edward/Jacob.
Swedish!Mokuba: Let's go find the genie voiced by Dan Ekborg, who also played Hades.
The name of Tel Aviv, Israel is a Woolseyism: the intent was to name the city after Theodore Herzl's book Altneuland (An Old-new Land), but this didn't translate well into Hebrew. Thus, to get the idea across, a combination of Tel, refering to an ancient archeological site in the form of a hill, and Aviv, spring (the season), which symbolizes renewal.
In fact, the name "Tel Aviv" came well before the city - it was the original name given to the book by its Hebrew translator.
Neopets does it with their own site sometimes, since some of the jokes, even when adapted, are still horrible as the original ones. But then, since Viacom expelled Adam and Donna from the team, it was just bound to happen.
When Coca-Cola first came to the Chinese market in 1928, there was no official representation of the name in Mandarin, so several shopkeepers interpreted it in different ways. While the right sounds (ko-ka-ko-la) were used, the wrong characters were used, giving us interpretations as "Bite The Wax Tadpole" or "Bite the Wax-Fattened Mare". Eventually, an official translation of Coca-Cola was used, sounding fairly close to its name (ke kou ke le) with the added bonus of meaning (more or less) "Tasty and fun" or more loosely/poetically, "Let your mouth rejoice". 
Isaac Watts' psalm "translations" for use in the Anglican church. Until the mid-1800s, the Anglican church didn't allow singing of hymns, but metrical translations of the Book of Psalms and other scriptural references were considered sacred enough for use. To hear Watts tell the tale, King David made direct references both to his own far-distant descendant Jesus Christ (by name, no less), and to the British empire - an international power ruling large amounts of land mass which were completely unknown to the Hebrews in David's time, seated in a nation that had yet to be created. Some of Watts' translations are still in use - "Joy to the World" chief among them!
The G.I. Joe franchise was renamed Action Force for the European market, because the phrase "G.I. Joe" wouldn't have meant anything to the non-American audience.
The Jonathan Coulton song "Re: Your Brains" has a French version ("Re: Vos Cerveaux") which replaces the line "All we want to do is eat your brains! We're not unreasonable; I mean, no one's gonna eat your eyes!"" with "On veut juste vous bouffer le cerveau! Non, ce n'est pas si bête; ca va pas t'couter les yeux de la tête!" This translates roughly as "We just want to eat your brains! It's not so bad; it won't cost you the eyes from your head!" However, in French, "couter les yeux de la tête" is an idiomatic expression for something expensive, similar to saying something "costs an arm and a leg."
When all of the Latin prayers and other parts of the Catholic mass were translated into various native languages after Vatican II, it was decided that more user friendly translations would be used instead of direct translations.
However, in 2011, extremely conservative Pope Benedict XVI, having thought the changes made in Vatican II were too radical declared that certain things (such as the Nicene Creed) be re-translated to be more faithful to the original, leading to a great deal of confusion as to what the word "consubstantial" meant and, in some cases, how to say it.
Manga on Danbooru is an interesting case. Usually the translators will try to keep it as close to source as possible, but occasionally this will happen, almost always with a note stating the literal translation.
The old idiom "When in Rome, do as the Romans do" makes this trope Older Than Feudalism. A direct translation would be "If you are in Rome, live in the Roman way; if you are elsewhere, live as they do there."