This happens to at least two characters in the film adaptation of 300; Stelios turns from a teenage Spartan who is ridiculed by the others when he tires out to an adult, battle-hardened soldier who exemplifies the Spartan image, and the Captain's son is given a name (Astinos) and takes Stelios's place as the eager young Spartan.
100 Bullets: Most of the Trust members (less than half of whom speak in their first appearance), although often just for the purposes of having a Death in the Limelight. Joan D'Arcy (the last member of the group to even be named, about ninety issues into the story) and Timo Vermeer are the main examples, with both taking the center to the stage near the end by the sole virtue of being among the only ones left, putting them into opposition with the Big Bad Ensemble.
Smithers, the Lodges' Butler, who gets a Day In The Lime Light narrating the fifth issue and backs Archie up on escaping Lodge Manor before the zombies overrun them.
Ginger, a rarely used side character, and Nancy, who has few appearances without her boyfriend Chuck, get quite a few scenes on their own before they join the main group. They're also secretly a couple.
Betty's obscure older sister, Polly, gets a fair amount of screentime in flashbacks.
Berrybrook Middle School: Every story focuses on a side-character from the last one. For example, Jensen was little more than a comic-relief character in "Awkward", only to become the protagonist of "Brave". Following that, Jorge's appearances in that story can be counted on one hand, and he is the central focus of "Crush.
Sonic the Hedgehog (Archie Comics) has done this to Muttski, Sonic's dog. When he first appeared in Sonic the Hedgehog (SatAM), he was just a random robotic dog. The comics turned him into Sonic's pet and remained that way until the recent Cosmic Retcon turned him into the Mobian Ben "Mutt" Muttski, Dr. Chuck's assistant.
These comics also later appropriated Honey the Cat, a Dummied Out character from Sonic the Fighters, and fleshed her out as a character by providing her with a backstory, a day job, and a reason to have temporarily joined the cast (she is an up-and-coming fashion designer who wants to promote her newest line to new audiences through a fighting tournament). The Archie team even created a CG model of Honey◊, updated to the Modern Era video games' style.
Fables had Nurse Spratt, who only had a couple of lines and appearances for the first two-thirds or so of the comic, until she betrayed Fabletown, changed her name and appearance, and revealed herself as one of the most unscrupulous villains in the whole series.
Karl Ruprect Kroenen from Hellboy. In the comics, he appeared briefly in Seed of Destruction, then figured in a minor subplot of Wake the Devil, at the end of which he died. In The Movie, he had as much screen time as the main villain, Rasputin, and his death was pretty ambiguous.
Despite being made a big deal of in early episodes of Jem, Synergy was mostly treated as a plot-device and rarely even appeared in her holographic form. In the comics there is much more of an effort to present her as a character and as family to The Holograms.
Craig appeared in under five episodes of the cartoon and is mostly treated as "Stormer's brother". In the comics he appears early on and it isn't even revealed he is Stormer's older brother until several issues in. They put more emphasis on his romance with Aja.
Clash is the Misfits groupie in the cartoon but only appears in a select number of episodes. In the comics she appears in almost every issue they do.
Roger was just a nameless bully in Ni GHTS Into Dreams, but is a major player in the Archie comic adaptation as he antagonizes Elliot and Claris and becomes a pawn of Wizeman and Reala.
The Red Dwarf Smegazine provides these for a variety of characters that varied from recurring characters (Ace Rimmer), to characters who only appeared in one episode (Mr. Fibble, Jake Bullet etc).
Sandra and Monique from the Scott Pilgrim series. Lampshaded in the final volume when they get multiple introduction scenes.
Parodied in the very first issue of Bartman #1 during the scene where Bart Simpson, Milhouse Van Houten, and Martin Prince all meet in the comic-book shop. Bart points out one comic's panel (unseen to the reader) featuring a street scene with a random pedestrian in the background. Bart explains that the writers plan to kill this guy off in the next issue and then bring him back to life as a supervillain known as "The Jaywalker".
The Star Wars Expanded Universe is famous for this, taking pretty much any and all minor characters from the films and giving them fleshed out backstories while weaving them into the mythos of The 'Verse.
Probably the most stunning example is Davin Felth; he's the random stormtrooper who says "Look sir, droids". The comics give him a full origin story, characterization, and show how he realized how monstrous the Empire was before pulling a Heel–Face Turn. He's also shown to have been present at every major event in the first quarter of Episode IV (such as the slaughter of the jawas and Owen and Beru's deaths, which were the Empire's Moral Event Horizon in his eyes) and is partly responsible for Luke and company escaping Mos Eisley, as he fragged his captain during the firefight in the hanger. All of this from an extra with a single line of dialogue.
Oroku Saki, aka The Shredder, was originally a one-time villain. However, he grew popular with the comic's readers. The rest is history.
In the original Mirage comics, Chet was the name given to the turtles' original owner, whose panel time can be counted on one hand. In the IDW comics, however, he is now one of Stockgen's head scientists, and April's supervisor.
Sunstorm of Transformers. In The Transformers, before the Decepticon roster grew enough to fill large battles with known characters, repaints of Starscream were often used when Megatron needed more Mooks. One of these repaints, seen very briefly in the premiere, was bright yellow. The comic books flesh out this blink-and-you-miss it extra into a radioactive berserker, and he's still getting toys and other appearances, and is homaged in Transformers: Animated (the kiss-up Starscream clone has his coloration.)
Another recolor, this one lime green and had no speaking part in the episode that originally featured him, was given the name Acid Storm and had a few appearances in comics and his own figure. He even got an homage of his own in the Aligned-continuity character of the same name.
Many, many Transformers have a role that's much larger than that of previous holders of the name. For example, Red Alert was a background character in a few episodes of G1, and his one A Day in the Limelight episode had him go insane due to damage. Transformers: Armada and Transformers: Cybertron make him The Medic and a central character. Also, Overhaul was previously a Redshirt in the Dreamwave Comics series: his first panel involved him getting a hole blasted through him.
The Transformers: More than Meets the Eye: Gives big parts to characters unimportant in all other adaptations: Like Swerve and Tailgate who debut as a group of Autobots shooting at Trypticon, here they're the Comedy relief team of a Motor Mouth Bar tender and a bot who's spent almost all of his life trapped underground having missed the war. Characters like Chromedome and Brainstorm, while important in other continuities, did almost nothing in the IDW series until this comic came along. Whirl was just a Wrecker with an interesting Cycloptoid design, he rarely had much characterization and died in many of his old appearances. Here he's become the Heroic Comedic Sociopath who's hated by all his co-workers and may have accidentally started the war by beating up Megatron. The Scavengers who existed before the comics were all marginal figures except Grimlock, and even in IDW, Crankcase's entire career was "fought Thunderwing and apparently died".
The Transformers: Last Stand of the Wreckers took a bunch of obscure background characters from The Transformers Marvel comics and updated them for their team: Squadron X. Ferak, a redshirt who exploded and died was retconned into being a different redshirt as well and Tornado, another one off character who, again, died in the old run. Now Botcon 2014 is pulling both into their space pirate story, mentioning their Squadron X days, and giving them both toys. Tornado even has a Facebook.
The Transformers: Till All Are One: Gives Blast-Off of the Combaticons a central role. While the Combaticons are one of the few Combiner Teams to avert The Dividual Often it was Onslaught, Swindle, or even Brawl who got the character-focus. In the IDW books alone Blast-Off spent most of his time as a background character and was absent from a few of the Combaticon's more important arcs. Here he's the most fleshed-out of the Combaticons as it's his machinations that kick off a good deal of the plot and his conscience that prevents more deaths from happening.
The Transformers: Autocracy: About all that can be said about Zeta Prime in the G1 cartoon is that he existed, and he didn't play much of a role in the IDW comics for a while due to having died early in the War. In Autocracy, he's the main villain up until Megatron kills him and takes the top spot, spending his time stomping about in a blinged-out Skeletor outfit and ranting like a cartoon supervillain.
The Transformers: Robots in Disguise: Buzzsaw had only a handful of appearances in the 2005 IDW continuity, only really showing up for group shots. Rumble and Frenzy received major characterization as some of Megatron's earliest followers while Ravage and Laserbeak were Soundwave's main minions for much of the early run. In RID, Buzzsaw is Suddenly Speaking and forms something of a Statler and Waldorf-esque peanut gallery with Laserbeak. He gets a few small moments of character in the present and the flashbacks had him alongside Laserbeak and Ravage as a trio rather than the duo the latter two normally had. Buzzsaw also ends up outliving most of his colleagues and survives the events of The Transformers: Unicron whereas Soundwave and Laserbeak die.
The Transformers: Windblade has Chromia in a prominent role, and she ends up being a central player in the story. In the G1 cartoon, she was just one of a handful of female Autobots featured in a single episode, and was largely known as "Ironhide's girlfriend". This carried through to IDW's second continuity too, where she's one of the most frequently appearing characters as Cybertron's head of security.
Wizards of Mickey: Fethry starts out as a One-Scene Wonder, but gets upgraded to recurring character, even taking Donald's place on the team on a couple of occasions.
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