Dragon Ball Multiverse: Universe 20 Broly. Salagir exaggerates Broly's power, moving him from "extremely powerful" to "invincible" while in his Legendary Super Saiyan state. Additionally, he gets a lot of focus despite being an ultimately unimportant character (his fight with Vegito being the Batman Cold Open of the entire series). This occurs because he thinks Broly's awesome. Broly is pretty unpopular with the hardcore Dragon Ball fanbase due to overexposure, so this blatant favoritism doesn't go unnoticed.
Zii from Ménage à 3 has attracted this label, at least in the comic's early days. There were a couple of reasons, but one large one was fan resentment of her convincing DiDi not to sleep with Gary, which was seemingly treated as perfectly valid; some readers didn't buy it. (Her reaction to Gary trying to draw her into a threesome with Amber also annoyed those fans.) Zii seemed to have perfect Karma Houdini status while being presented as a Lovable Sex Maniac, without any acknowledgment that her "hilarious" exploits maybe went too far. That said, there were fans who liked her, and discussions about her made her a Base Breaker. Eventually, Character Development happened, as some of her actions developed significant consequences. Things like the appearance of her secondStalker with a Crush, her wall-climbing frustration at DiDi's antics, and her burning jealousy of Gary's sudden desirable status, left her looking far less casually invulnerable and made many of her detractors lose their vitriol.
Meanwhile, in the same comic, Yuki has also attracted the same accusation, as her sometimes very violent actions never seem to attract realistic consequences.
Claire of Questionable Content is starting to draw accusations of this from the comic's fans. She's not a bad character in and of herself, but once she and Marten hooked up the Perfect Sweetness of their relationship started to grate. Not helping matters was Marten suddenly developing the ability to glare relentless and omni-offensive robot-pervert Pintsize into silence when the latter started to make Claire the target of one of his comments, and Marten laughing hysterically for apparently hours following a rather lame pun on Claire's part.
Makoto Yosue of Red String morphed into this over time. The author originally admitted she put him in to act as an obstacle and antagonist to the original Official Couple, but later interviews included statements such as him being her favorite character and getting very defensive on some occasions when he received criticism. He started getting a ridiculous amount of Character Focus for a supporting cast member (which on the official web site, he still listed under this category) and time spent on his supposedly horrible life (consisting of simply being sad a girl dumped him once) while other plots more important to the overall flow were getting ignored. As the series moved into its finale, suddenly everyone was talking him up, including characters that either never met him, or had met him when he was in his previous "jerk" characterization and had no reason to suddenly think he was a good person. For example, Miharu's parents constantly talk about what an outstanding worker he is, but he's never seen doing anything more than being a waiter, something Miharu and Karen do without thanks or praise for the entire comic. The fanbase pretty much turned on him when his characterization fell apart and he became controlling over Miharu to the point of screaming at her in public for continuing to associate with her old boyfriend (a relationship Makoto never once respected when it was in progress) and stalking her old boyfriend at work and insulting his suicide attempt only weeks after he got out of the hospital.
Xanthe Justice from Sinfest (aka "Trike Girl"). She hit this trope by being the in-universe catalyst for a Base BreakerRe Tool, plus an unhealthy dose of Writer on Board. For nearly a year, she was riding around talking about the "Sisterhood" taking down the "Patriarchy," trying to recruit female characters and talking down male characters. She remains in Mary Sue territory most of the time. For example, she gave a rather physical Get a Hold of Yourself, Man! to the hand of God.
"If you come into Unsounded thinking I want you to forgive Sette her foibles because she's so cute and because I've stuck her in the lead, you got the wrong idea. But it's my fault if they get the wrong idea 'cause I'm the one givin' out ideas! Some people just can't enjoy a heroine with the issues that Sette has. And I absolutely get that. Funnily enough people have short memories and when Murk was introduced it's like they thought here's another morally reprehensible character that Glass fatuously expects us to adore. But no, dorks, he's just a morally reprehensible character."