When it first hit Japanese airwaves in 1971, Lupin III (Green Jacket) was met with quite some controversy – the content was more adult-oriented than what was usually allowed on the air – and eventually succumbed to low ratings, being cancelled after just 23 episodes. Reruns then led to a considerable increase in popularity and it is now considered a groundbreaking classic, spawning a diverse multimedia franchise with two sequel series, a handful of movies, and dozens of TV specials. Lupin III: The Woman Called Fujiko Mine actually gets away with much of the adult-content it has because of the fond memories Japan now has for the original anime series.
This also happened to The Castle of Cagliostro. Hayao Miyazaki's first film flopped when it first ran in Japanese cinemas in 1979, due to being much Lighter and Softer than typical Lupin fare. Fans stayed away from it, and no one else had any reason to check it out. It was only years later, once the film found an audience outside Japan and Miyazaki had made a name for himself with Studio Ghibli, that people rediscovered Cagliostro and gave it its current status as one of the true Classics of animated film.
In the English-speaking world, licensors have been trying to market Lupin since the early 90's, but always fell short of achieving the popularity they wanted. Lupin III (Red Jacket) got an airing on [adult swim], but due to a two-front backlash by modern anime fans against the dated animation and by longtime Lupin fans who hated the dub, the show's ratings were low and it was cancelled after airing just 30 of its 155 episodes. Its video release was halted not long after. Even so, that short run was enough to finally earn Lupin a large enough fanbase to justify a small licensing company, Discotek Media, releasing every Lupin anime it can get its hands on.
Mobile Suit Gundam, one of the most influential Humongous Mecha series ever, was cancelled three-fourths of the way through the show and given a completely different ending as a result, albeit one believed by many to be superior. Once it entered reruns, it suddenly became tremendously popular and spawned a countless number of sequels and spin-offs (this is one of the major reasons Gundam has been described as "Japan's Star Trek").
G Gundam and Gundam X were not well received on their initial release, with Gundam X being the first (and to date only) Gundam show since the original to be prematurely cancelled. Now they are thought of as among the best entries in the franchise. In a complete reversal, the manga spinoff of Gundam X even had its run extended due to being unexpectedly popular. The same could be said for Turn A Gundam, which over time has come to be seen as one of the best in the franchise.
While it still remains one of the more contentious entries in the franchise, Gundam SEED Destiny tends to spark far less hate and Internet Backdraft than it did when it first released. The series' and characters' improved handling in Super Robot Wars, coupled with the even more widely-hated Mobile Suit Gundam AGE have led to a sizable portion of its former hatedom giving it a re-evaluation—many of them still don't like the series, but it draws nowhere near the level of vitriol that it used to.
Dangan Ronpa 3 has a minor example. The ending is still controversial and the issues pointed out are still there and still bother fans, but the following installment, New Dangan Ronpa V3, was so divisive and the fans hate the ending so much that DR3 got fans back for this.
Space Runaway Ideon was in a similar mess, but the fans caught on this time and it was given a full movie for its Grand Finale, despite being cancelled with only a few episodes left.
Averted with Super Dimension Fortress Macross, yet another highly influential series. After languishing in Development Hell for a couple of years, the series finally got the greenlight, but was cut down to only 27 episodes. However, the series proved popular enough that it got an extension to 36 episodes halfway through its run.
The Vehicle Voltron didn't enjoy half the popularity of the Lion Force Voltron. But that's only because it followed the Lion episodes in most markets (in some, it was shown in bits and pieces between several Lion episodes). The Vehicle series wasn't "bad" by any stretch. It simply had the unfortunate tendency to be compared to the "cooler", but more formulaic, Lion series. Kids of that time latched on to the Lion series probably because it had elements that they already identified with: Fairy tales (magic, castles, princesses, evil rulers) and superheroes (the Super Robot and the Five Man Band). Vehicle Voltron was adapted from the more Military Science-Fiction show Dairugger XV, presenting a more mature Hard Science FictionStar Trek like format. It also had a lot of characters to keep track of on both sides as well as presenting a lot of shades of grey instead of good vs. evil. Kids just weren't yet ready for a cartoon that had a lot of character relationships, politics, and subplots. It was the early 80s after all. Kids like their formulas. They just wanted to see "action". But then Robotech would come along and then they'd be ready. Now Vehichle Voltron is looked at as wrongfully underappreciated. One will also now notice that Dairugger was far less Bowlderized than Golionwhich even in its original form was formulaic Monster of the Week.
Until a couple of years ago, you couldn't say that you remotely liked Bruce Faulconer's soundtrack for Dragon Ball Z. To utter such words would have you mocked for enjoying music that was inferior to the original track and make some fans question your fandom. Now, Bruce Faulconer's scores are fondly remembered, especially Vegeta's Super Saiyan Theme, Ginyu Transformation, Goku's Super Saiyan 3 transformation, and DBZ Finale. Even those who overall enjoyed the Japanese track better have their favorites and those who don't like Faulconer's work do show some appreciation. Most of this new respect happened because of Kai, which originally had a completely different, divisive, and blatantly plagiarized soundtrack by Kenji Yamamoto. Some fans even wish Faulconer would return to Dragon Ball, thinking his score would go great with Kai. Don't believe us? A simple search of "dragon ball kai with faulconer score" on YouTube should bring up plenty of proof.
Dragon Ball in general was this to Western viewers. There have been multiple attempts to bring the franchise stateside, but all have failed. The Harmony Gold dub never officially aired. The Ocean Dub of Dragon Ball only lasted one season before getting cancelled. A year later, they skipped to Dragon Ball Z, and while it lasted longer, it got cancelled on a cliffhanger due to airing at a poor timeslot. When Toonamipicked up DBZ, the ratings skyrocketed, which allowed the show to get revived with a new English dub by Funimation.
While Dragon Ball GT is still mostly disliked, or at least considered So Okay, It's Average, the Super Saiyan 4 transformation is generally considered to be one of its best contributions to the overall lore. When it received canon counterparts in the form of Super Saiyan God and Super Saiyan Blue, the SS4 form set itself apart with its more imaginative design and the fact it recalls the association between Saiyans and Apes. GT also has the fewest continuity errors, but this didn't save the series from being hit with Canon Discontinuity to make way for Battle of Gods, Resurrection F, and the newest television series, Super.
My Neighbor Totoro, one of Hayao Miyazaki's greatest works, failed to turn a profit on its first release in 1988. Two years later, King Totoro dolls became a hot-selling item and the film gained a re-evaluation, raising Miyazaki's esteem on an international scale.
Its failure in the initial run probably had something to do with the fact that it was bundled with Grave of the Fireflies, one of the most depressing anime in history.
In another Ghibli example, Disney's dub of Castle in the Sky commissioned Joe Hisaishi to rerecord his score with a symphony orchestra exclusively for their release. Miyazaki himself approved of the end result. So did certain critics. Many, many American purists, however, were furious, instantly condemning the new score as "a crime against all humanity." The Ghibli Blog infamously even called both the dub and the rescore the equivalent of Nausicaä of the Valley of the Wind's first American dub, "Warriors of the Wind." Perhaps because of this, Disney reissued the dub without the rescore. Although today there are some fans who still bitterly resent the rescore, ironically, its removal from the dub has caused other reviewers to give it a second evaluation; many recent reviews of the film and the redub now declare the new work as one of the dub's biggest assets, as well as a genuine improvement over the original. Even the rescore has a following of fans, many of who were saddened when it was jettisoned. In fact, the rescore received a soundtrack release in Japan! Up until 2017, the only way to view the film with the rescore was to import the BD from Japan, the UK, or Australia. Gkids has since reissued the film on Blu-Ray, providing viewers with the opportunity to see the dub with either score.
A bizarre mixture of this and Germans Love David Hasselhoff, The Vision of Escaflowne. It actually bombed during its initial run in Japan (it was seen as a ripoff of Fushigi Yuugi), but it proved popular overseas. Likewise, in America, the series was actually cancelled just halfway through its broadcast run. However, the American series – at least as aired on television – was a Macekre. Once people started to see the uncut dub (as well as the subs), it became an anime classic.
Similar to the Escaflowne example above, albeit to a lesser extent, Ie Naki Ko Remi (or Nobody's Child Remi) was the last series from the World Masterpiece Theater before their ten year hiatus, and WMT was already having problems before then. The show did horribly in Japan, suffered from despicably low ratings, and was brutally lambasted for massive changes from the original Hector Malot book (like changing the main character into a girl, removing the boat, and expanding on one small part of the story and running with it all the way through). The critical reception was so bad, the final three episodes never aired on TV and were straight to DVD instead. Thankfully, thanks to a devoted fansub group, some international attention, and more appreciative fans, it has gotten more positive reception in the form of fans viewing it as its own entity as a cute, charming, somewhat dark series, a good show in its own right, and don't mind that it's not faithful to the source material. Those who like the source material try to view the show as a separate entity and appreciate what it does well, rather than nitpick at everything it did wrong.
When Digimon Tamers first aired, many fans of the Adventure series were disappointed and confused by the lack of relation between the stories, and much of the themes and subtext were lost on younger viewers. Over a decade later, thanks to both access to the Japanese version and a higher demand for more cerebral, deconstructive series, Tamers has gained a large amount of popularity, and is easily the second most popular Digimon series.
The Transformers Unicron Trilogy. Armada was downplayed due to its Gotta Catch 'Em All attitude with Mini-Cons, and Cybertron for its limited animation. However, both have picked up in popularity due to later season story lines, and "Ambush" is considered to have some of the best CG of ANY Transformers media up to that the time. Energon however, still tends to be received rather poorly.
In the realm of Pretty Cure, we have Futari Wa Pretty Cure Splash Star. Initially, the series didn't do well, and until Suite Pretty Cure ♪ came along, this series had some of the worst ratings in the franchise's history (though even then, it still did much better then most other series that aired at the time). It was also seen as a bad Retraux of the original two seasons, having the two main character being Nagisa (Saki) and Honoka (Mai) expies, and also garnered some detractors for toning down the realistic Seinen elements of the original, as well as favoring zippy flight and beam spam over hard hitting fisticuffs for quite a bit of the show's run as a result of Moral Guardians attacking the original show and its sequel. After Growing the Beard, it still never made as much money as the original series or series after it ever did, regardless of quality (even when it didn't make 10 Billion Yen that year, it still made more money then most other big anime franchises could even dream of making, just not as much as what Toei wanted). As the years have gone by since then, however, the fanbase sees the series with much more prestige, due to managing to make Saki and Mai their own characters, Michiru and Kaoru being the first true Dark Magical Girl characters introduced in the franchise, the latter half of the series gaining back some more classic elements, like hard hitting attacks, and many of the elements introduced here being mixed in with these original elements, setting new standards for the series to have when it comes to the fight scenes, and the villains as a whole are considered much more memorable, well written, and generally menacing in their own way and not too wooden either. It is currently held on many fan lists as amongst the best seasons in the franchise, alongside the likes of the Ensemble Darkhorse of the franchise, Heart Catch Pretty Cure, which says quite a bit for the series after its initial sour reception amongst the fanbase.
A rare character example: Minmay from Robotech was one of the most hated characters ever, partly due to her whiny voice provided by Rebecca Forstadt (who, to say it politely, was not the most suited actress for the role), the bad quality of her dubbed songs, and her overall ditziness. But over the years, people who once hated her have now warmed up to her and see her more as a goofy but good-hearted girl who was unable to cope with the insane situation she found herself in.
That ADV Films was given the go-ahead to make an uncut dub of the original Super Dimension Fortress Macross and cast Minmay with an actress who actually knew how to make her likeable (Mari Iijima, her original Japanese VA) didn't hurt either.
Idolmaster: Xenoglossia was bashed by fans of the original game for being an In-Name-Only adaptation when it first came out. Nowadays it's seen as a more decent robot anime as long as you don't consider it as an adaptation of IDOLM@STER. This is mostly because there has since been a more faithful adaptation and because Xenoglossia was directed by Nagai Tatsuyuki, who later went on to direct other animes, most notably Anohana.
The Pokémon anime's Orange Islands arc was originally disregarded as Filler that didn't really amount to anything since the Gym challenges weren't always actual battles and the League itself wasn't based on an in-game region. Nowadays, whenever a debate starts concerning Ash's competence as a trainer, people will often mention it immediately, since his victory there technically means Ash qualifies for the title of Champion, and that also marks the first real sign of his growth as a Pokémon Trainer. It is also pointed out that the Orange Islands brought several fan-favourites such as Ash's Lapras, Ash's Snorlax, and the Crystal Onix, and that the battle between Ash and Drake was the series' first full battle.
More fans overtime have been starting to consider the controversal Black and White series an example of this trope. While it did several things wrong, particularly with Ash, it also did several things right that have continued to be done to great effect in the subsequent XY and Sun and Moon series - namely, a better series structure and pace, a more faithful rendition of the region from the video games, the regular formula for Filler episodes being mostly dropped in favor of more inventive situations, Team Rocket not appearing in every episode and not taking up too much unneeded time in episodes they do appear in, Team Rocket being more competent, and introducing much longer story arcs (the Meloetta arc and the Episode N arc) which were the predecessors to the Z arc of XY and the Cosmog arc of Sun and Moon. Some will argue there were even things that it did better than other series, such as a more even group dynamic. Essentially, it is viewed as the reverse of Franchise Original Sin - even if it is not considered good overall, it originated many popular trends used in subsequent entries in the series.