Unsurprisingly, it's a bit rubbish. At least, in the Game of Thrones department. Because according to this chart:
+ Sansa is LESS LIKEABLE than Joffrey. Only marginally less likeable, but they're already pretty much as far down the "likeable" index as it's possible to go. Even if people don't like Sansa as a character, are we really saying that we hate a girl who is being held prisoner and forced to marry into her enemy's family MORE than a boy who kills beloved characters, has extended sexual torture scenes, and is generally a psychopath?
+ Arya (who it seems is the most likeable character) is AS GOOD as Sansa and Jon. I'm not saying that Arya isn't an amazing character with lots of justification for her actions, but even in the show (where her brutality is toned down a lot), she is starting to display some really brutal tendencies, like her murder of some of the Freys at the end of the last episode, or even her williness to have her own personal assassin in the second season. She's not an evil character, but she hardly ranks on the purest end of goodness.
+ Daenerys, meanwhile, is both a lot less good and a lot less likeable than Arya, although she's still in the positive section for both of those traits. Surely Daenerys' actions place her about equal with Arya in terms of goodness, if not higher, since she always has good intentions?
+ Cersei is both MORE EVIL and MORE HATEABLE than Tywin Lannister. In the show, Cersei's been reduced to a character who killed an innocent Direwolf, plotted against her husband, was involved in Ned's downfall two years ago, and is really mean to Sansa (who, we've already established, is hateable anyway). Tywin just organized the slaughter of hundreds of people, including several Starks, at a wedding. He told fan-favorite Tyrion that he should never have been born and ordered him to rape Sansa. He's an interesting character to watch, and might rank as "I hate him but I love to see what he's going to do," but less evil than Cersei? Really?
+ Jaime is significantly more likeable and significantly less evil than Cersei. I'm a massive Jaime fan, as are many people, so I can understand ranking him highly on the likeability scale. In fact, my only question there is why he's significantly less likeable than the Hound. But again, why is Jaime, who shoved a child out of a window and crippled him, without remorse, considered significantly more good than Cersei? In book world, through A Dance With Dragons, I can see where this comes from. But based on what we've seen on screen so far? They're both pretty culpable.
+ Cersei is more likeable than Sansa. Because naively contributing to your father's death (if we accept that argument, although I don't) and then struggling to survive in the resulting mess is far worse than actually being one of the orchestrators of that murder. Or something.
Obviously, the chart means nothing in real world terms. It isn't a declaration from on high about which characters are acceptable and which aren't. But it is pretty revealing about the way that we view and rank female characters, both compared to one another and compared to male characters. Arya, as the tomboy character, is given massive leeway in terms of being a "good" character, because we want to see her fight and be brutal and get revenge. Daenerys, a character who does battle and fight, but is generally elegant and sophisticated and steps back from the violence itself, is considered less likeable. And Sansa, the actually "good" Stark sister, in terms of high morality and kindness to others and a tendency not to kill people, is not only on the opposite end of the likeability spectrum to her "not like other girls" sister, but more unlikeable than the show's actual most evil villain. And why? Because she makes mistakes that are "girly," such as being a bit of a dreamer, and being optimistic, wanting Joffrey to be her prince and wanting the stories to be true. And now, I guess, because she fights back using courtesies and subtleties and words, like Cersei, rather than with a badass backflip and a sword. Cersei, meanwhile, is the most evil and unlikeable Lannister (Joffrey excluded), even when most of her evil actions in the second and third books are given to her son, because she plays the game using smiles and manipulation, rather than the bluntness of Jaime or Tywin. She's a woman, and non-fighting women who act feminine get less leeway in terms of being morally grey.
I don't know enough about any of the other shows featured to comment (although I believe viewers of Breaking Bad may have things to say about the placing of Skylar), but the results for Game of Thrones here are as depressing as they are predictable. Tomboys are awesome, noble girls are stupid, and if you're going to be do something people won't like, try to be a man. It's far more forgiveable that way.