Takua in BIONICLE started out as the Featureless Protagonist of a little-known Game Boy Advance game. After he was again the main character in a very successful online game (moving from AFGNCAAP to having his own identity only at the very end), his popularity exploded. In 2003, he was the star of his own Direct-to-Video movie where he became Toa Takanuva and was released as a toy set twice (once as Takua and once as Takanuva). Then he and the other 2002-2003 characters returned in 2008 (complete with new toy figures), with Takanuva being the star of the first Level 3 Readers book and having an online blog that narrated the events of the final (regular) book. And his was the largest figure. He was released again as a Stars commemorative set in 2010.
Also of note are the Toa Inika. When the story moved to a brand new location (Voya Nui) in 2006, LEGO decided that, rather than create six new Toa characters, they would just take probably the six most popular Matoran characters (Jaller, Hahli, Hewkii, Kongu, Matoro and Nuparu) and turn them into Toa, via space lightning.
Equally significant is the 7thPirakaVezon, a character who was an accidental clone of one of the other Piraka. He was the 2006-2007 Big Bad, but was just so wacky that fans loved every appearance of his, whether he was drafted to free an offscreen former Big Bad who defected pre-series, or simply went on madcap interdimensional adventures.
A very minor on-line game character, called Tiribomba, developed a small following, despite having done absolutely nothing to contribute to the plot. The reason for his popularity lies in his wicked awesome name.
The Barraki as a group quickly shot to this position in comparison to the other Quirky Miniboss Squads released before hand, partially due to the fact they completely broke the mold of having the same body type and each had a unique build to them, and partially because their backstory and connection to Makuta made them compelling villains. The fact that they were not affiliated with Makuta's plans at all but were running against them and even had intentions for the Mask of Life that extended beyond just gaining power and even successfully getting it at several points made them even more interesting, to the point they were brought back in the web serials.
All the promotional Good/Bad Guy freebie sets are generally seen as "So Bad, It's Good", but the 2006 version in particular became especially well-liked, partly due to embodying all that's wrong with these toys, and party for his appearances in the popular Reviving BionicleFan Film comedy series. So much so that he's become a meme years after the toy line had been canceled, and fans have been creating or even army-building their own versions of the Guy.
The Alley Viper figure from the original G.I. Joe line has a huge cult following amongst GI Joe fans, to such an extent that it was quickly re-released within two years of its initial run in circulation.
Same with the Crimson Guard figures; this was most notable during the GI Joe Vs Cobra/Valor Vs Venom years, when Hasbro built a new Crimson Guard mold and opted to not release as part of the regular series, opting to make the figure a Toys 'R Us exclusive. To ease fan anger, the figure was largely released in a series of army builder sets, meaning fans buying the figure could build their own units without having to buy multiple figures.
Mimic, a garish green unicorn from the 1980s My Little Pony line, reportedly did poorly in sales in her initial run. On today's second-hand market, prices soar. It's been speculated, though, that Mimic's poor initial sales are what made her so hard to come by, and are the reason for her value today. (Another likely reason is her odd color scheme, since there are very few green ponies.)
Firefly may be the queen of this trope. From the moment she was introduced, she was arguably the most popular of all the ponies. Even though she wasn't in much of the series, having one TV special before getting the Brother Chuck treatment, and having a reoccurring role in the British comics, she was depicted on a ton of merchandise. When Rescue from Midnight Castle was rereleased on video in the 1990s, it was renamed Firefly's Adventure, even though Megan is really the main character. Lauren Faust even based Rainbow Dash's personality on her. (She would have been Firefly if not for copyright issues).
Wind Whistler is the second most notable generation one pony after Firefly herself. Her stoic and logical personality contrasting with the happy-go-lucky others made her reactions to their usual antics hilarious to watch. Having a good amount of sarcasm and pointing out Fridge Logic at their expense.
Generation 1's Fizzy, with her bubbly personality, pretty much shares her popularity with Wind Whistler above.
Minty from the third generation line stood out as The Ditz, in an already eccentric cast of ponies. Her obsession with mints and collecting socks were seen as particularly endearing.