Suzaku and Kallen
At first they did not get a lot of interaction. For the first half of the first season, the only interaction they go was in their Knightmare Frames, trying to kill each other basically.
When Suzaku first came to Ashford Academy, Kallen sympathised with her fellow Japanese. She did not join her classmates' gossip about Suzaku. When Suzaku joins the Student Council, the two become slightly more aquainted.
Their relationship probably really starts in episode 19, where the two are stranded together on an island. The two battle with their different views about Japan and Britannia. Suzaku knows that captured terrorists don't end up well, that her methods see no future. But Kallen knows that being a servant of the Britannians, has no future for her. However high a status that Suzaku has become, an Honorary Britannian citizen, a Knight of the Third Princess, Kallen believes it is nothing; Samurai Kururugi didn't live on as well.
Despite their different views however, Kallen and Suzaku manage to become honest with each other. Kallen's true nature is revealed, and she is surprised when Suzaku calls her more "charming" that way. She tells him that she needs to change the wrongs in the world, otherwise her brother's death would have been in vain. But I feel this relationship was much more important for Suzaku. Kallen is the first person that Suzaku willingly tells of his father's death; that he killed him. His emotions poor out of him, and that he doesn't want anybody else to choose the wrong path, where only emptiness and regret will lie.
Whether he said this because he felt connected with Kallen, or if it was just in the spurr of the moment, this was an important step for Suzaku. He freely admits that he killed his father, and the pain and suffering he felt as a result of his wrong decision, the wrong path he chose. This is something he has never told anyone else.
And again, Kallen says something that really makes Suzaku think. She asks, what her brother lived for, and who is to decide what's right and wrong. Kallen's brother was living for what he believed was right. Suzaku wonders what he is living for.
After the Stage 19 island incident, Kallen believes that Suzaku will reveal her identity; she states in Stage 20 that she can't return home or to school. She confronts him in Stage 21's School Festival and asks why he hasn't revealed her identity to the authorities. Suzaku tells her, that on the battlefield and Kozuki Karen, he won't hold back. But at school as Kallen Stadtfeld, he will continue to persuade her to quit terrorism. He knows it's against the rules, but decides that it's what he wants to do.
Later in the festival, Kallen is surprised that so many Elevens have arrived at the school festival. Sayoko explains that it's Suzaku's school, and Suzaku is like a symbol of hope for the Japanese people. Kallen watches the happy faces of her people cheering at Suzaku, and maybe starts to feel differently about Suzaku.
However friendly they had become at school, once on the battlefield again, they are relentless. The two battle fiercely, holding nothing back despite their relationship. Suzaku has held Lancelot's gun straight and Kallen's Guren, with every intent and no hesitation to kill.
