Bravomaster from the Bravoman webcomic is a heroic example, while his enemy, Zulu, still get's some funny moments from beating up the Bravo corps. they combine into Bravomaster and toss him into the sun, the lack of jokes on panel is later lampshaded. Later, Bravoman get's transported to an alternate universe where the world has been destroyed. Zulu had come to Earth and forced everyone to team up to stop it, having done so, Dr. Bomb unleashed his army on the heroes, shutting down the fourth wall and preventing any gag-based powers or easy victories. Earth has been reduced to a wasteland and Dr. Bomb was deposed long ago, and it was really the version of Anti-Bravoman who had done all of this, from unleashing Zulu, to shutting down the fourth wall even to attacking Salaryman and imprisoning him. It was all in the quest to become stronger, and in the end the heroes have to return the meta-humor to the strip to stop him.
Ann Walker from But I'm a Cat Person: it was around the time we learned more about her goals that the mood of the comic took a sharp turn from a fairly light-hearted fantasy comedy to a dark urban fantasy adventure.
Borzax from Cloudscratcher, though having the courtesy to make his mark relatively early in the story.
The only somewhat-serious The Dragon Doctors gets a lot more heavy once the Crax chapter begins. It's a horrible flesh-and-mind-devouring parasite, and it's followed up on with a serial killer who kills people with nightmarish death spirits, a Die Hard scenario in a hospital, and tragic backstory after tragic backstory.
The first two of the Four Fiends, Lich and Kary, are played as fairly serious villains, with their presence resulting in major character deaths (and in the case of Black Belt, Killed Off for Real) and some dramatic moments. The later two, Ur and Muffin subvert this trope, with Ur being killed in an Anticlimax while the Muffin Arc is dealt with humorously as usual.
And then we get Black Mage's "Almighty wizard of infinite evil"-form, which, unlike all other "evils" up to that point, actually causes a major Cerebus Syndrome and manages to kill off half of the cast in less than 10 comic strips before squaring off for the final battle with a powerful wizard. Until Sarda comes in and reveals his plan, that is.
Damien is a great example of this trope, to the point where the author killed him just to stave off Cerebus Syndrome. It didn't really work, as the series has since entered Cerebus Syndrome from a different angle.
Abraham was supposed to be even worse, but the whole thing turned out to be one huge misunderstanding on his part, and after everything was explained to him, he surrendered without further fight. He even got to be funny in places, something that did not apply to Damien. Pandora seems primed to do this in-universe, as she seeks to give her son a world where he can make a difference.
Given the ever-escalating nature of Homestuck, there are at least three "candidates" throughout the story so far: the meteor at the end of Act 1 (not a character, but the moment where things start to shift from inventory shenanigans to plot), Jack Noir in Act 4 and Lord English, or alternatively his servant Doc Scratch in Hivebent/Act 5.
The Midnight Crew intermission also had one with Snowman. While the Felt were otherwise portrayed as hilariously incompetent gangsters existing only to mess up with their time powers before getting killed by the Midnight Crew, Snowman came in, and spent the rest of her screentime horribly maiming the fan-favourite main character.
Lord English could count as this. Before his appearance, every major villain had some sort of comedy to them. Bec Noir wanting bones like a dog would, Doc Scratch as serious as he usually is has some humorous lines. Lord English has yet to do anything supposed to be perceived as comedic. In fact, the first thing he does after his introduction is to go and kill the author, who was absolutely terrified when he appeared. He then proceeded to presumably erased many dead characters' souls from existence with a single mouth laser. Although, his younger self is quite a humorous villain.
The Wanderer, better known as The Cheese, from It's Walky!. Anyone who can be ominous and badass even when people refer him as "The Cheese" is obviously not someone to trifle with.
Ozimaar appeared unexpectedly on page 14 after 13 silly comics and created a nonsensical storyline which lasted 'till December '07 when the author cancelled the arc and skipped on ahead in the story, because the Ozimaar Arc was boring him.
Then Computer re-appeared rampaging through the ongoing story lines and twisting them onto her self.
Kiwi Blitz features the villainess Gear,whose presense is currently the only source of grimness and darkness in an otherwise fun and whimsical webcomic.
Last Res0rt was already pretty dark, but by the time we bring Veled around... she's the Big Bad, and she doesn't leave much doubt of it either. Even if she does have more comedic value than most as she's easily bored (and eager for entertainment), Veled never comes off as harmless — in fact, when she's bored, she's even more dangerous.
Jeff from RPG Worldkills Eikre's family and makes some pretty disturbing scenes, giving a whole lot of drama to a webcomic parodying classical RPG cliches.
Sam and Fuzzy takes a turn for the serious which is arguably kicked off by Fridge. Although he starts off as comic relief, his actions in the "Friday Night" arc drag Sam into the Ninja Mafia plotline that has dominated the last four years of the comic.
Schlock Mercenary has played with this trope before, but it didn't stick until the introduction of Admiral Emm. ExtremelyDangerously Genre Savvy, the only reason the Toughs weren't immediately compressed into neutronium and fed into an annie plant was because Admiral Emm wanted to let Colonel DeHaans torture them first, just to make sure her clean-up job on Laz'R'Us nanite information was complete and thorough. The Toughs only survived by handing over an expert on immortality treatment and agreeing to let the UNS mindwipe them. The fact that the very next story arc was the darkest story arc by far didn't help anything.
Xanthe from Sinfest brings in the Sisterhood arc after which much of the series' humor has vanished. An interesting example in that she doesn't seem to be a villain, though her extremist views tend to annoy the fans anyway.
Despite only appearing once so far, the hooded archer from Slightly Damned counts. Devenol even more so.
Sluggy Freelance kicks its Cerebus Syndrome off with a Mook vampire named Kullan. He fits this trope because his introduction is (a) pretty much the first strip in the series to end on an ominous note rather than a straight-up funny one, and (b) the start of the "Vampires" arc, Sluggy's first more or less serious storyline.
As the strip progressed, the presence of Oasis, K'Z'K or HeretiCorp is a fairly good signal that a given arc is going to be darker than usual.
Dr. Schlock may qualify. Not only is he involved in virtually every other arc's sinister events, but even his first, still-comedic appearance, as a scientist testing cosmetics on Bun-bun (or, well, trying to), sets up numerous events in the series, including the nanomachine plague. It's not clear if that cosmetic lab (which also did nanomachine research) was part of HeretiCorp or not (and, if it was, if it had been all along, or if Abrams decided retroactively that it was).
Colonel Glass from Spinnerette. Before, all the series had for major antagonists were Dr. Universe, Alexis Woodrow, and Captain Alberta - a noble Well-Intentioned Extremist, selfish Attention Whore, and incompetent Politically Incorrect Villain respectively. Glass? An out-and-out Ax-Crazy sadist who kills and skins animals to send messages - a modus operandi disturbingly similar to that of the notorious House Bolton. Glass is also notable for being far more powerful than most supers in the Spinnyverse. In a setting in which most characters have abilities like moderate super-strength, a weaker and more realistic version of the Spider-Man power set, or sonic punches, Glass is essentially Magneto with Wolverine's Healing Factor: he can control glass with enough power to chop up people and vehicles in seconds and create near-impenetrable shields, and enough finesse to grab hostile drones in midair and send them crashing into their controllers, not to mention regrowing lost limbs and shrugging off whole-body third degree burns.
Zebra Girl has always kept a somewhat uneasy balance between funny and dramatic, but it tilted firmly into dramatic territory (and ditched some of its sillier, Fourth Wall-breaking gags) with the appearance of Harold DuVase. This is kind of odd, since DuVase appears at first to be a Harry Potter parody. In the end, he turns out to be something much, much worse...