One of the relationship dynamics in the show that I like the most is between Jaime and Brienne.
However, I have not read the books. Is their relationship built on (slowly-built) respect for one another, or is there anything else happening?
Mutual respect slowly builds after Jaime suffers his disfigurement. Suddenly he is no longer the cock on the walk, able to do what he wants to whomever he wants. He is no longer the shining golden perfection. Because he is now imperfect in his own eyes. And Brienne is also imperfect, both being a woman knight and described as highly unattractive. Because he can see them both as disfigured, he can now see them as something approaching equals. It is a measure of his respect for her that he gives her his sword.
Keep in mind, Jaime started as a two dimensional character but developed into a far more complex, three-dimensional character. He isn't entirely a bad guy, especially once he learns imperfection.
I thought the show emphasized more of a sexual attraction between them than was present in the books. There was some in the books, but I thought that was more due to Jaime coming to care about Brienne (because he now respects her) and being that she is perhaps the second woman in his life that he's ever really cared about, even he isn't sure about his own feelings.
Consider, he loves his sister and knows their love is forbidden. He cares about Brienne, and in his eyes (because of her imperfections) their care and respect for one another would be forbidden. With his sister, he just goes and consummates. He doesn't with Brienne, but he may well feel that he should, because that's what he thinks he is supposed to do with women he cares about and respects. I think that even Jaime isn't sure about his own feelings; he has some kind of emotions and he isn't entirely sure how to deal with them.