This is a tough one for me. I too will break this down by DA iterations.
DAO:
Oghren: I really didn't like the personality of DAO Oghren much at all. It was painful to have to take him along during the Orzammar sections, and he was just ...a whiny #$% most of the time. Mechanically he was a fine party member, but I really didn't like him much because he was just plain rude, coarse, and not at all the kind of person I would hang around with. He wasn't necessarily badly written, just not someone I liked.
DA2:
Fenris: "I'm so ANGRY" seemed to be the order of the day with this guy. There was no depth to the character, he was just an emo-angsty self-entitled little ******. Maybe it's just that I have outgrown the teenager mindset, but it felt like I was babysitting a sullen neighbor's Jr-High school son, the kind that always "knows more about the pain of life" than anyone else and thinks his limited life experiences are the breadth of everything. I liked aspects of his character design and dialogue, but he just was such a pain to deal with, that I ended up leaving him behind on almost every mission.
DAI:
Cole: I have never had such an outright HATRED for a character until Cole. I despise this character for so many reasons, but most of all because of his 'special nature'.
I will explain a bit more, I used to help storytell and admin for the old Camarilla Roleplaying Fanclub for White Wolf's World of Darkness, and there was a certain type of player that we'd inevitably encounter over time, that we'd call 'Crayon-Eaters". These players would commonly mistake eccentricity and childishness for immersive roleplaying, and so would define themselves through 'cutesy' acts and strange behavior, rather than actually flesh out their personality. They would play the role of the 'innocent', the naive, the mentally-disturbed, the 'damaged-goods', and expect to be protected by others, to be shepherded by other players, and to be reluctantly reactive to story and plot rather than proactive. The 'strangeness' of their behavior came to define them, rather than their actual actions and they often lacked character goals beyond 'being weird'. Through their eccentricity, they would expect the spotlight and center-of-attention, because otherwise if they were ignored in favor of you-know, actual plot, they were exposed as being rather shallow and empty of any group-dynamic and contribution. In essence, there's a strong bit of Mary-Sue and Larry-Stu qualities that comprise a 'Crayon-Eater' and they require and demand quite a bit of plot armor and narrative protection to function.
Cole embodies so many of the same tropes and tactics of the Crayon-Eater, that it's impossible for me to not see the parallels even at a glance. I understand that he is further fleshed out in the novels, but upon a cursory read-through, I saw more of the same 'broken' behavior and character qualities that turned me off of Cole in the first place. I don't think that he is a very well-written or strong character, but rather is a caricature of a character archetype, and not a particularly good one at that.
Coupled with his INCREDIBLY offensive character trait of invasive mind-reading everyone at all times, not just without their consent but actually against their stated objections to "Get Out Of My Head!" and I find the character to cross over the line of simply being shallow and tasteless into confirmed CREEPY MIND-RAPIST. I don't find him endearing at all, rather I find him repulsive and my first instinct each time he loads up in-game is to want to squash him like a vile roach. What makes things worse is his habit not just of mind-raping people, but of exposing their secrets constantly and with a smug sense of almost-malice. He's like a 'Damien' style of EVIL.
I don't know why some people find Cole lovable, huggable, or endearing. I can't imagine why Dave Gaider or Patrick Weekes felt that writing him in the manner chosen made for a better character or how his invasiveness into the private thoughts and memories of others is somehow justifiable or excusable in the context of a 'heroic' character or protagonist's companion. Unfortunately there is no way to kill/destroy Cole, so my solution has been to never open or pursue "The Forgotten Boy" mission, leaving him to remain a nonentity in my subsequent playthroughs.