While I confess I sometimes found Jaime amusing and his chapters compelling, I never "liked" him. He flung a small boy to his death, or at least he hoped to.
I cannot condemn Theon for the Miller's boys and not condemn Jaime for Bran. I think they are both paying for their crimes, but that does not make me like them.
I have had compassion for the women in their stories - Brienne and Jeyne.
Killing children and hunting people with dogs puts you past the pale. I am looking at you Cersei, Jaime, Theon, the Hound and Ramsay. (I have probably forgotten a few.)
Qyburn and his Mengele-like experiments also turn my stomach.
When you get right down to it, most of the characters have done something I find objectionable, but Ramsay is the one I find most vile.