Watch out for spoilers
Cassandra - I respect the character's conviction and fortitude. I love how dynamic she is, especially with her interactions with party members. She has a purely good heart and is willing to admit her mistakes.
Dorian - this character also has strong convictions. He chose to leave behind a lavish life because he didn't want to live against his heart. He is, imo, the most courageous character by standing up for his beliefs against an entire nation. I also really liked the dynamics between him and his father during his personal quest. Not to mention, his party banter is so enjoyable!
Sera - I didn't like her at first, but I think that's a testament of how well written her character is. There is a method to her madness, but in the end it's all serving to help everyday people. She's especially intriguing if you listen to the banter between her, Cole, and Solas (on mobile, no spoiler tag know how, but if you are aware of the tinfoil, you know what I'm talking about). I'd totally hang with her on a roof irl).
Solas - I was really moved by his stories of the fade (I wish there were more!). His motivation in the breadth of the story is so interesting once you get to the ending. I adore the murals he creates in Skyhold. I really enjoyed his lines during Cole's personal quest (forgiveness path).
Blackwall - I love stories of redemption (and the way he calls my femquisitor "my lady" - she melts every time). His interactions with Sera are fantastic; you get a sense of his nurturing, fatherly nature. He is incredibly funny.
Cole - Just a fascinating character all around. His dialogue is always intriguing and I love how clueless he is sometimes. My favorite Cole moment is definitely the end of wicked grace (it comes off!?).
Cullen - I respect his character's extraordinary strength - his ability to push on despite past and present pains (tortured for days/weeks in the tower, betrayed by his commander in Kirkwall, his addiction during inquisition) is inspiring. Also, he's a total babe.
Iron Bull - I love his sense of humor, and the way he treats the chargers is super endearing.
Vivienne - She's a bitch, but so very witty. I love her banter. When your inquisitor befriends her, she is much more endearing and soft. I like her unique stance on the temper mage conflict and find myself agreeing with her on more than a few occasions.
Varric - Honestly, after the events of Kirkwall, he just seems checked out emotionally. For me, he is the most boring of the characters - I think it's because his personality is so static by comparison. Don't get me wrong, he was my fave in da2. He just lost his luster.
Josephine - yawn. Plus, her accent gets really annoying really quickly.
Leliana - Her bloodlust is very disturbing, especially when comparing to her younger self. It's ironic that during her personal quest, she notes that Justinia loved her compassion before straight out icing her "sister". I don't like her at all. Though, I know it's directly relative to how you handle her first cut scene.