A question to the Cat partisans: put yourselves in Cat's shoes at the end of the Robert's rebellion, when Ned comes home with a bastard boy.
a) realise that the child is blameless and accept it and love it?
b ) hate the reminder of your husband's infidelity but realise that the child is blameless and accept it into your household?
c) hate the reminder of your husband's infidelity but realise that the child is blameless and allow it into your household while making sure it knows the hierarchy?
d) hate the reminder of your husband's infidelity, hold it against the child, making sure it feels as hated by you and unwelcome as possible in your household, treating it worse than you treat the servants?
Irrespective of historical context, I think you'd have to be a pretty shit human being to choose d.
Not that I think that Cat was a bad mother (clearly, it's blasphemy to say a bad word about Cat...), but she was responsible for Ned going south to act as the Hand and her rash actions in going south incognito/capturing Tyrion did endanger her family for no gain. I'm not saying that she should have gone all Red Wedding on the Lannisters, but perhaps with a little more calculation there would be more Starks alive now. She abandoned Rickon who has now grown up pretty wild, relying on a brother a few years older than him to be a male role model, which is a lot of responsibility for a young boy in a coma (Maester Luwin and other household staff were servants and not appropriate role models before anyone says it). While I don't think it's likely that she would/could have stopped Theon and the Ironborn, it's not unfeasible, and at least her two boys would have had their mother, instead she dallied in Riverrun - understandable but I think her boys needed her more than her father did.
And then there is her treatment of Jon Snow. I don't really need to mention anything more about this, especially as all Cat's fanboys and girls have justified her behaviour to themselves and are convinced they're right on this. All I'm going to say is that in my opinion, and it is just an opinion, her treatment of him does not become a lady of otherwise good character and is an irredeemable blot on it. Blaming a child for the father's sins is hardly noble behaviour.
There are so many characters that I find really interesting and that's the great thing about the series - that there aren't many proper characters that I really don't care about. When I say proper characters, I mean people who are named and have an actual story, not those who are named but we know nothing about except that they did 'x', like Ser Willem Darry. In terms of dead by the start of AGoT...
Most: For the sake of not repeating the fairly standard Starks and Rhaegar (though I want to know more about them!) I would really really really love to know more about the Night's King. Less far back in history, the Hound's father - what kind of parent creates the Hound and the Mountain?
Least: any character like Ser Willem Darry who have no point except to provide a detail in some other character's story. Catelyn Stark's mother. Theon's brothers.