There are some interesting relationships in the show. I'd say if these were real people, they would make therapists some of the richest people in the world. But don't get me wrong, that is what makes the show so much fun. If people were normal, then what would be the fun in that? Also, as this is a discussion of the relationships between characters, there are some spoilers. No major ones though.

Akio and everyone else
I just have to say this... Yes he has. Yes, with everyone. >=D

Nanami and Touga
One might say Nanami has a slight 'big-brother complex' However, its stops there >.> Nanami does NOT want anything sexual with her brother...she's not that warped. Ever since they were young, Nanami has looked up to her brother. From what I can tell, she only had him growing up. She thinks Touga is the greatest person in the entire world. Not just the greatest, but so great no one else can compare. She hates the girls that fawn all over him. She exacts revenge on one of her 'henchmen' for sharing an umbrella with Touga. However, she does this because if someone else takes Touga's attention, she's 'lost' the only brother, the only sibling, the only one she's ever been close to. Its not just humans that she treats this way. When a pet cat began taking more and more of Touga's time, Nanami became jealous then too and threw the cat into a river. I'm not saying Nanami is kind, but her relationship with her brother is only platonic.

Saionji and Anthy
When Saionji was the current victor in the very beginning, he treated Anthy poorly. He hit her and yelled at her and it was you basic abusive relationship. Every so often though, there were indications that he really did care for Anthy. When he had been expelled and was staying at Wakaba's, he asked Wakaba how Anthy was doing in a very quiet, calm voice. While everyone else talked about themselves getting to the castle above the arena by winning Anthy, he was the only one to say he wanted to go to the castle with Anthy.

Juri and Ruka
Juri and Shiori are talked about everywhere, but seldom is Ruka mentioned with Juri. Ruka was the former fencing captain, and even when he came back, Juri deferred to him as the captain. But Ruka did not leave the hospital where he had been for months merely to duel for himself. While he was back at Ohtori, he forced Juri to face the truth about her and Shiori, and about herself. At the end of Juri's second duel with Utena, she merely ripped the rose off her chest and dropped in on the ground. She no longer needed to gain the power of Dios, either to disprove miracles or to gain Shiori. At the hospital, nurses commented that a young male patient had died, but that he was glad to have seen someone one last time and set them free.