Zii from Ménage à 3 is rapidly becoming a Creator's Pet. There a couple of reasons, but the big one was convincing DiDi not to pop Gary's cherry, an overarching theme of the comic. Her argument was that Gary would keep coming back to her begging for sex, though she didn't have any actual basis for that claim. Plus, like almost every interaction she has with DiDi, it comes off as another one of Zii's attempts to sleep with her. Fans were not entertained.
Worse than that, Zii only very rarely receives any punishment for anything she does, no matter how dickish or possessive. The comic often tries to present her as a wacky, Lovable Sex Maniac without acknowledging that her "hilarious" exploits often go too far. That said, there are fans who like Zii, and discussions about her get very intense, making her a Base Breaker. Still, the affection the comic has for her and refusal to punish her makes her a Creator's Pet to fans who don't like her.
There was a recent arc in which Gary was invited into a threesome with another man and asked if the man could be replaced with Zii, who has slept with the woman. Later Zii then berates Gary about this and states that she would never try to force someone into a sexual situation for her own satisfaction... despite that this pretty much sums up her character in a nutshell.
Also, of course Broly would fit the bill. It isn't helped even though is surviving a powerful attack was explained.
Vriska Serket from Homestuck was accused of this quite frequently. The author's story he is that he wanted to write a highly divisive character, which amounted to making an egotistical, malicious yet not entirely unsympatheticpsuedo-Sue and having her hog massive amounts of screentime and plot relevance, up to and including romantic interest with the main character. Reactions varied from fan to fan, and even after her character arc's conclusion, while not nearly as detested as in her peak, she remains one of the most strenuously debated aspects of the comic. Which seems to be just as the author wanted it.
The so far unnamed Trike Girl from Sinfest became one of these pretty quickly. In 2011, she shows up and begins talking about the "Sisterhood" taking down the "Patriarchy." Almost every other second of her screen time is just her riding around trying to recruit female characters and talking down male characters. And while the Sisterhood has become kind of an annoying Plot Tumor, it's all compounded by the fact that, so far, none of it seems to actually be going anywhere. The organization's entire contribution to the plot is making Monique come off as almost paranoid, a reference to The Matrix that was an Overly-Long Gag months ago, and the final straw leading to Fuschia's Heel Face Turn, which admittedly is one of the better moments in the comics and something many had been hoping for, but it still could have been done in a better way. Trike Girl herself has received, at the very most, almost no Character Development, despite the fact that the some-odd year she's been around is more than enough time to give her some, meaning that even now, she's basically less of a character and more of a rolling plot device.
