I can't pin down an overall favourite, and my likes are different based on the books and the show. For example, and yeah, SPOILERS, I really like Brienne in the books but I don't like her in the show because in the books she hasn't killed the true king of the Seven Kingdoms, Stannis the Mannis. But I have a few who are right up at the top.
Arya Stark
I always like female characters who are a bit tomboyish and I'm drawn to female assassins in fiction often. Right from the start (in books and show), Arya rejected the life of a noble lady and wanted to learn how to fight, not how to sew. As a daughter, she's more alike to her dad, Ned, than her mother. Because I love Ned and hate Catelyn, that had an influence on me liking Arya early on. What I like about her is that, while her arc has seen her become an assassin who lives for nothing but violent, bloody revenge, she isn't just a killing machine. In the show at least, she only kills people she has a reason to kill. I was very pleased she wouldn't kill the actress because it was cold-blooded and would have made Arya a murderer. I know she murdered Meryn Trant and Walder Frey and a lot of other people but she had a personal reason for those murders and so, to me, they were justified within her storyline. She isn't indiscriminate, she is focused. The Starks have had a rough time throughout and it's great to see them taking back control and working against their enemies. Arya is very much taking back control in a very direct way, and it's an arc I love seeing.
Jaime Lannister
I will be the first to admit it: Jaime Lannister is a handsome devil and that is a big part of why I like him so much, in the show at least. But beyond that, Jaime is great. I like him more in the books, overall, but he's one of my favourites in the show, too. He has a really well-developed arc of being a total b*stard who cares only about himself and his sister, to being more aware of the world he lives in and his effect on it. When he loses his hand, he loses who he is. He has to learn how to fight again, even learn how to write again, and his outlook on himself and his place in the world changes. He considers the grander picture of his actions instead of just on showing off, and he's becoming something of a good diplomat. His relationship with Brienne is engrossing because she's teaching him about honour, a concept he, as a knight, should have always been familiar with. And that relationship is changing him into a more complex, interesting, well-rounded character. In the books. In the show, there's some movement in that direction, but he's still very focused on him and Cersei above all else. Compare that to the books, in which Jaime and Cersei are drifting apart because he's becoming more compassionate towards the people while she is becoming more megalomaniacal. It feels like the show won't commit to uncoupling him from where he started, so I rely more on superficial traits to like him as much in the show. And by superficial traits I mean his face. His handsome face.
Davos Seaworth
If you don't love Davos then get out of my face. Davos lives in a world that is so hostile and unforgiving and cruel and yet he is so good, so just, so hopeful for the best. He's a voice of reason, a hand that guides the sword. He knows that the people are the key to the kingdom and it is them he thinks about when he supports Stannis the Mannis. Davos is a voice of reason in an unreasonable world, and it's so necessary to have someone who cares so much. He is an anchor, he wants for the world to know peace so much that I can't help but moor myself to him as my moral centre in the books and show.
Some honourable mentions: Jorah Mormont, Tyrion Lannister, Sandor Clegane, Tywin Lannister, Varys, Mance Rayder.