She struck me as a good character in the beginning of the book (well, she is a good
character...) but as the story progressed and I learned more about House Stark and its dynamics, I began to have less and less respect for Catelyn.
In the beginning, when she goes to Eddard in the weirwoods at Winterfell (I believe they were somewhere near the Heart Tree at that) and she talks to him for a while, I thought that she seemed like a caring mother and wife, all in all a good character in the making and a generally good human being.
As the story progresses, though, and you learn about Jon being a bastard child and you see more of Catelyn around Jon himself and just the concept of him, she just sort of loses my respect because she's so unnecessarily cruel to Jon and was so confrontational about his existence with Ned. The scene when Jon is about to leave to go with his uncle Benjen to the Wall, and he stops to say goodbye to a sort-of comatose Bran, Catelyn just tells him to leave and is positively vicious and stubborn on the whole topic of his presence there. What's especially offensive about this part is when Catelyn tells Jon to leave (for sort-of the third time, notably.) and immediately follows it up with, "We don't want you here." That was so wholly unnecessary and cruel to Jon, that she spoke for his unconscious half-brother (who had always treated him like a full-blooded brother, to my knowledge) and said something of that nature.
It's understandable that Catelyn is hurt by Jon's existence, as he was born a bastard while she was married to Eddard and he was away at war or something of the like, but she has no reason to be angry at him. He didn't ask to be born a bastard; if anyone deserves her malice over such a thing, shouldn't it be Eddard instead? Eddard was the one who couldn't keep it in his pants while he was away, and that's not Jon's fault, he just happens to be the result of it.
The whole issue of Catelyn wanting Jon sent away is a bit strange, from my point of view, though I can understand the logic behind it, it's sort of an archaic way of dealing with something like that... I don't know. My take on this is that she should take Ned's insistence that Jon live with them at Winterfell as some sort of reassurance that he honestly loves his children (...of which he happens to have four by her, I believe), and while she doesn't necessarily have to love Jon as her own or anything of the like, or even at all, I think she should at least treat him like a fellow human being.
But that's just my take on the whole thing... what's yours?