When it first hit the Japanese airwaves, 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. Reruns then lead to a considerable increase in popularity and it is now considered an anime classic, spawning a diverse multimedia franchise, with two sequel anime, 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. It also helps that a small licensing company, Discotek Media, is licensing 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 ∀ Gundam, which over time has come to be seen as one of the best in the franchise.
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 Vehichle 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.
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.
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 enough overseas to now be considered an anime classic. Likewise, in America, the series was actually canceled. However, the American series was a Macekre, but once people started to see the uncut version (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 theming and subtext was 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.
In the realm of the Pretty Cure franchise, 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 franchises history (Though even then, it still did much better then most other series that aired at the time). It's 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 shows run as a result of Moral Guardians attacking the original show and it's sequel and after Growing the Beard, it still never as much money as the original series or series after it ever made, 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 of 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 were 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 Dark Horse of the franchise, Heart Catch Pretty Cure, which says quite a bit for the series after it's 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 (the QUEEN of the Bratty Half-Pint voice), the atrocious 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.