Recursive Import

So you made this neat videogame, right? But, hey, this game may just be too Japanese or just too weird, or you used a copyright license in a certain region you can't use in another, and apparently in order to sell it outside the region, you need to, um... change it. The plot, the main characters, or the soundtrack could all be candidates to be adjusted, possibly for the sake of a Dolled-Up Installment.

Sometimes this can lead to a very strange conclusion—the altered version of the product being marketed alongside or after the original version. Will lead to the inevitable stupid arguments over which version is better.

Note that this is different from more standard imports in that it's the selling of an alternate-region version of a product that originated in the country of question. Also, selling a faithfully adapted alternate-language version does not really count—although a Macekre-ified version might. This trope applies best when the product is radically changed and yet the source material is obviously traceable.

Related to this trope is "reverse importing". Since American anime DVDs are far cheaper than Japanese ones, some Japanese anime fans choose to import American DVDs to save money. This eventually led to Bad Export for You.

Examples of Recursive Import include:

Comic Books

There was a 70s manga version of Spider-Man by Ryoichi Ikegami that was partially translated during the late 90s under the title of Spider-Man: The Manga. This was before Ikegami developed his hyper realistic art style.
The Japanese X-Men manga (1990s in Japan) was similarly translated, at the same time. Unfortunately, the Hulk manga (1970s) never made it over.
The Bat-manga: Japanese versions of Batman produced during the '60s "Batmania" craze. Some of these stories were translated into English and republished in the book Bat-manga.

Film

Many U.S. remakes of French movies made it back to France. Some were hailed, others bombed.
The British version of The Magic Roundabout movie is available in the United States as Sprung!, alongside the US Gag Dub version Doogal.
When Godzilla: King of the Monsters was released in America, a new character was edited into the film, an American reporter played by Raymond Burr. It was later released in Japan under the title Monster King Godzilla, with Burr's dialogue dubbed into Japanese. It was so popular that it started a trend of reporter characters in Kaiju films based on Burr's character.
The ancient Chinese legend of Hua Mulan was adapted into a film loosely based on the legend. The film was then dubbed into both Cantonese and Mandarin and released in China.
The American live-action version of Fist of the North Star was dubbed in Japanese with some of the original voice actors from the anime providing the voices of their characters. Namely Hideki Kamiya and Toshio Furukawa, who dubbed the voices of Gary Daniels (Kenshiro) and Costas Mandylor (Shin) respectively.

Literature

Several books from the apocrypha were originally written in Hebrew, but then lost over time as they did not form part of the Jewish Biblical canon. In modern times, some of them have been translated back into Hebrew from earlier translations, such as Greek.

Live Action TV

Super Sentai shows got revamped into Power Rangers for the USA... for a while Power Rangers was dubbed for Japanese audiences, complete with a cover of the classic theme song by Masaaki Endoh. Also, as in the below Kamen Rider Dragon Knight example, one character was voiced by the Japanese equivalent- in this case, Machiko Soga, who played Bandora in Kyoryu Sentai Zyuranger, was the Japanese voice of Rita Repulsa.
- Power Rangers SPD is getting this treatment, complete with Dekaranger actors dubbing their SPD counterparts (with the exception of Swan's counterpart Kat, in which the original actor Mako Ishino is unavailable, and then they call in Rie Tanaka to stand in for her).
- Mako Ishino, in turn, gets to have the opening narration.
- Power Rangers Mystic Force is the next to be dubbed. This time, the Magiranger actors don't get to voice their counterparts, but at least Atsushi Hashimoto (MagiRed) gets to do the narration.
When Takeshi's Castle was distributed outside Japan, the British version just had Craig Charles narrating the footage, while the American version changed it into MXC: Most Extreme Elimination Challenge. MXC was a parody of Game Contest Shows and Reality Television which featured deliberately bad overdubbing and lots of low-brow humour. This Gag Dub was later re-imported to Japan, where it actually became more popular than the original show.
Common with British shows adapted for America. The BBC ran The Weakest Link USA alongside The Weakest Link, and Little Britain USA underwent the same treatment.
The United Kingdom also gets the U.S. version of The Office (as The Office: An American Workplace) on DVD.
$ale of the Century was a game show that was originally created in the USA, then exported an Australian version. Years after the original US version had ended, the Australian version was exported back to the US, resulting in the better-known US version that starred Jim Perry. Years later, the Australian $ale was revamped into Temptation, a Spiritual Successor, which was then exported back to the USA as Temptation: The New Sale of the Century. The exported versions were quite successful and arguably more popular than the original US version, except for the US Temptation, a low-budget Macekre that barely resembled the original show or Aussie Temptation.
Hells Kitchen was initially a UK show (with celebrities), but changed significantly in its export to the USA (with competition between professionals for a job). The US version now runs alongside the UK version on its original channel, and is more popular and successful.
Kamen Rider Ryuki was adapted for America as Kamen Rider Dragon Knight. Dragon Knight was then dubbed and aired on Japanese television. Many of the dub actors are Kamen Rider alumni, but for bonus recursion points the character of Len/Wing Knight was dubbed by the actor who played Ren/Knight, his original equivalent.
The original American Gladiators was so popular in the UK, they made their own version. When the 2008 American reboot came along, they incorporated many trappings of the UK version, including some UK-only events, into the remake.
American Idol aired alongside its original, Pop Idol, in Britain.
Ninja Warrior, the American airing of the Japanese show Sasuke, itself is shown in Japan. This includes the changed format and editing, and the new "Ninja Killer" and "Warrior Wipeout" segments added to the show. This actually makes some sense, since Sasuke airs as annual multi-hour long tournaments. By showing Ninja Warrior in Japan, fans can rewatch older tournaments, and the broadcasters can make more money airing the show as a regular episodic program.
The two foreign Ultraman shows, Ultraman Towards The Future (Australian) and Ultraman The Ultimate Hero (American), were released on home video in Japan as Ultraman Great and Ultraman Powered respectively.

Theatre

The famous aria "Avant de quitter ces lieux" from Gounod's opera Faust was originally written for a London production. Its words ("Even bravest heart may swell") were in English, and only subsequently translated back to French.
Similarly, various portions of Richard Wagner's Tannhäuser were rewritten for the Paris production, and the words had to be retranslated into German.

Toys

Originally, Hasbro manufactured G.I. Joe toys, which were sold in Japan by Takara. Takara later introduced a new toy to the line called Henshin Cyborg, whose Gimmick was that he was a robot who could turn into a car. They then ran with this concept and created the Microchange and Diaclone lines, and a bunch of other companies copied them. Hasbro later introduced redecos of these toys into America under the name Transformers; when they proved popular, Takara re-imported the American toys into Japan, where they outsold both Diaclone and Microchange.

Video Games

Doki Doki Panic was revamped into Super Mario Bros. 2 for the USA audience—then released in Japan as Super Mario USA. The remake of the Japanese SMB2 (essentially a Mission Pack Sequel) that was part of Super Mario All-Stars was eventually released in America as Super Mario Bros.: The Lost Levels, though the original 8-bit version was eventually released on the Wii's Virtual Console outside of Japan (although the Virtual Console release is also referred to as The Lost Levels in the Wii's menus, the game itself was unchanged, so it still says Super Mario Bros. 2).
- A more subtle Super Mario Bros. example came much later during Super Mario 64's localization, when Nintendo of America decided to add lots of new voice clips - for instance, Princess Peach reading her letter at the beginning of the game - and make other minor changes. When Japan got a re-release of Super Mario 64 supporting the Rumble Pak, the American tweaks were finally carried over.
Not quite, but close: Osu! Tatakae! Ouendan is mostly entirely revamped into Elite Beat Agents. While the latter game is not released in Japan as far as I know, the characters have cameo'd in Ouendan's sequel as well as in Super Smash Bros.. Brawl.
- Though EBA's improvements were carried over into Osu's sequel, and are unlockable in it.
Life Force, the American version of the Gradius spinoff Salamander, changed the plot of the game by setting it inside a giant space creature that has been infected by a killer virus. Aside for a couple of background changes, the American Life Force was otherwise identical to Salamander (and the NES version of Life Force had only very subtle differences from the Famicom version of Salamander). However, an Updated Rerelease of Salamander was released to Japanese arcades under the Life Force title, actually changing the graphics to give the stages and enemies an organic look, as well as changing the power-up system to the one used in the Gradius series. Salamander and this version of Life Force have turned up together on Compilation Rereleases.
- The JP rerelease and the NES version further changed the story by setting it inside a Unicron-esque Planet Eater named Zelos.
The obscure Konami arcade game Mikie, High School Graffiti is actually the international version of Shin-nyuu Shain Tooru-kun ("Tooru the Freshman Employee"). Both, the Mikie and Tooru-kun versions, were released in Japan.
The Taito NES game Power Blade is a heavily Americanized revamp of Power Blazer, which was originally a rather blatant Mega Man ripoff. Apparently Power Blade proved to be a bit more successful than Power Blazer, causing Power Blade 2 to be released in Japan as Captain Saver.
Square Enix has done this several times, starting with Final Fantasy VII International when all of the additions made to the North American version were imported back to Japan...with further additions (most notably a bonus disc). The example that causes the most ire though is Kingdom Hearts II Final Mix+ which gave the Japanese fans everything the North American fans had in their version plus extra bosses and storyline scenes. This version of things ended up being a case of No Export for You for the American fans.
Animal Crossing for GameCube was Doubutsu no Mori + with a bunch of new furniture, new holidays, and e-Reader support. This version got translated back to Japanese with even more stuff as Doubutsu no Mori e+.
When the original Metal Gear Solid was released overseas, the developers added adjustable difficulty settings, a hidden Tuxedo outfit for Snake, and a "Demo Theater" that allows players to view all the cutscenes after completing the game once. All of these extra content would be introduced to Japanese players via Metal Gear Solid: Integral, which also retained the English voice acting from the American version.
- The Japanese version of Metal Gear Solid 2: Sons of Liberty: Substance also qualifies, since it included English voice acting in place of the original game's Japanese voice acting, as well as the European Extreme difficulty setting from the PAL version.
- On the other hand, in the Japanese version of Metal Gear Solid 3: Snake Eater: Subsistence, all of the extra content from the European version is included, but the voice acting is still in Japanese.
In Japan, the Street Fighter Alpha series is known as Street Fighter Zero. When Capcom released the second installment in America, naturally titled Street Fighter Alpha 2, it added Evil Ryu to the character roster, as well as bonus versions of Zangief and Dhalsim based on their Champion Edition selves. Capcom then re-released the game to Japanese arcades under the title of Street Fighter Zero 2 Alpha, which featured all three extra characters from the American version (giving Evil Ryu his own ending), along with added Champion Edition versions of Ryu, Ken, Chun-Li, Sagat and M. Bison. This version was then ported to home consoles as Street Fighter Alpha 2 Gold, where Cammy was added to the roster.
De La Jet Set Radio is an Updated Rerelease of the Japanese version of Jet Set Radio. It included extra songs, two levels, and, most importantly, bug fixes from the American and European versions.
A truly bizarre example is the Takarazuka musical based on the Gyakuten Saiban series. Despite the musical being a case of No Export for You the musical used the names from the American version, Ace Attorney, possibly to avoid Japanese copyright issues.
Fist of the North Star: Ken's Rage, the English version of Hokuto Musou, was released in Japan as Hokuto Musou International.
The fourth Kunio game for the Famicom, Nekketsu Kōkō Dodgeball Bu: Soccer Hen ("Nekketsu High School Dodgeball Club: Soccer Edition"), was released in modified form outside Japan as Nintendo World Cup for the NES, which had the various Japanese teams redesigned into international ones for the overseas version. When Technos developed a Game Boy port of the game, they took the World Cup theme from the NES version and made all of the rival teams into foreign ones, retitling the game Nekketsu Kōkō Soccer Bu: World Cup Hen ("Nekketsu High School Soccer Club: World Cup Edition").
The Sega Mark III game console was redesigned into the Sega Master System for the western market. Sega later released an updated Mark III model in Japan based on the Master System redesign, but with an integrated FM sound module (which the western models did not have).
The Super Famicom puzzle game Panel De Pon was released in the west as Tetris Attack for the SNES, with the original fairy characters replaced with the characters from Yoshi's Island. The overseas version was later released in Japan for the BS-X Satellaview under the name of Yossy no Panepon.
The Toaplan shooter V-V was released outside Japan as Grind Stormer, with a different powerup system that provided bombs instead of weapon upgrades. V-V for the Japanese Mega Drive provided both games in one cartridge; so did the American Sega Genesis version of Grind Stormer, which in fact was the exact same cartridge in different packaging.

Western Animation

Cartoon Network announced at Anime Weekend Atlanta that it is indeed working on acquiring the U.S. rights to Powerpuff Girls Z. (Whether the negotiations actually succeed is another story, of course...)

Multi

The word "Mecha" is derived from the English word "mechanical".
The name of the Irgun, one of the Jewish underground groups fighting in the British Mandate of Palestine, is an anglicism meaning "organization". The word is the gerund of "le'Argen", a modern Hebrew neologism meaning "to organize", formed by placing the consonants of the English word "organ[ize]" into a Hebrew verb structure.
The name of Cuba's newspaper Granma is simply a variation of the English word "Grandma", taken from the name of the boat that brought Castro to Cuba in 1956.
Star Wars is a series of movies that originated in the US. Then, several manga artists did manga adaptations that were sold in Japan. Then, the manga were translated into English and sold in the US.
Japanese-market versions of American-made vehicles, like for example the Jeep Cherokee, made their way back to the States as they have found a niche with rural mail carriers due to their right-hand drive configuration, which saves postal workers the trouble of reaching to a curbside mailbox.

Other

Parodied in this Nerf Now strip.