Connor is a fictional character from Angel the series, which was created by Joss Whedon, who also created Buffy the Vampire Slayer and Firefly. If you haven't seen Angel, stop reading now, as everything from here on in is a spoiler.
The delectable Vincent Kartheiser in my opinion did an excellent job of portraying the character of Connor.
Connor is the son of two vampires. Vampires are usually sterile but for complicated reasons, Connor was born. Darla, his mother, died giving birth to him. Angel, his father, was raising him when he was abducted as a baby by Holtz, an enemy of Angel's, and taken to a hell dimension.
Holtz's family had been murdered by Angel back in the days when Angel was evil. Kidnapping Connor is an act of revenge. Holtz raises Connor to hate and fear Angel, even though Angel now has a soul and works to help people, rather than eat them.
When Connor reappears in Angel's life, due to the differing rates at which time passes in our reality and in the hell dimensions, Connor is a teenager, although only a short time had passed from Angel's point of view.
Things get even worse when Holtz follows Connor back from the hell dimension and continues to lie to and manipulate him, even to the extent of committing suicide and having Angel framed for it.
In a lot of ways, Connor is a dark mirror of Buffy. Because of Connor's unusual ancestry, he is strong and fast like a Slayer and has excellent demon-hunting skills, to the point where he has been nicknamed "The Destroyer" by demons.
But, although he has the agility and innate skills of a Vampire Slayer or a warrior, he hasn't the mental armour that her safe and oblivious upbringing gave Buffy, or the protection the certainty of her mother's love allowed her. She also had friends and family, and knew that she was one in a long line of Slayers who came before her and who would continue after her. Connor is the only one of his kind, which is a lonely thing to be. Buffy has Giles and the Watchers to fall back on, and although that is a relationship that is not without its problems, at least the infrastructure exists. When Connor was growing up in a hell dimension, he had no safety, he had nowhere he could forget the danger he was in, he had no certainties, except perhaps hatred. It's like he's missing a layer of skin.
Due to his extremely turbulent childhood, Connor is filled with confusion, anger and grief. In this, he is very like every other teenager on the face of the planet; however, due to his particular situation, it's not just a natural rite of passage he's going through. He really is conflicted and traumatised. He really can trust no one.
Over the course of the series, and now in the After the Fall graphic novel series which continues the stories of the characters, Connor's character's growth and development is very realistic, even though he's a character in a fantasy series. So much that he can tolerate Jasmine's appalling true appearance (which is scary when you think of it -- how bad can his upbringing in the hell dimension with Holtz have been, that he can put up with that?) for the sake of gaining some peace of mind in her presence. He even did his level best to kill Angel when his soul is displaced temporarily, but Faith managed to stop him.
Even though he is a killer and doesn't hesitate to do dreadful things (such as locking Angel in a coffin and throwing him in the ocean, or murdering a girl so that Jasmine can be brought forth, for example), sometimes flashes of the regular boy he never got a chance to be show through, as when he is so puppy-like in his interest in Faith and Cordelia. Or when he sasses his father:
Connor: What's a zombie?
Angel: It's an undead thing.
Connor: Like you?
Angel: No, zombies are slow-moving, dimwitted things that crave human flesh.
Connor: (smirking) Like you.
Angel: No!
Even for a survivor like Connor, his experiences are a long slow downward spiral. Eventually he reaches a point where the weight of all his horrific experiences at his young age is too much for him and he wants to end it all.
That's probably the main reason I like Connor. Despite the circumstances of his birth, he behaves like anyone would. He reacts to hellish circumstances in a realistic way. He's the classic abused child: edgy, dark-hearted, always terrified. He's lied to and isolated and threatened all his life, driven to violence and torture and murder, finally to suicide.
Buffy has a Destiny as a vampire slayer and rises to the challenge; Angel is fated to be a vampire and, through repentance, rises above it; but Connor falls, and falls hard. That is why he is a character I can believe in.
Essentially Connor is a young man who has had too much weight put on his shoulders: it warps him.
But once given a fresh start by Angel's sacrifice in the episode Home, Connor becomes a rounded individual -- the brave, loving, good-natured boy he always should have been.
Connor makes peace with his conflicted heritage eventually, I think. In Origin, he tells Angel, "You do what you can to protect your family. I learned that from my father." In Not Fade Away, the series finale episode, Angel knows the last battle is near and so Angel goes to visit his son. Later that day, Connor shows up at Angel's offices just in time to save Angel's life. When Angel asks him what he's doing there, Connor says, "Come on. You drop by for a cup of coffee, and the world's not ending? Please."