Yuki and Tohru
Yuki and Tohru are both kind hearted people, so it's only natural that the two of them would become close. Before Tohru began living with the Sohmas, she only knew Yuki as "the prince" and Yuki only knew her as another girl. However living with each other has made them see past all of that and the two have become close friends.
The two of them are very comfortable around the other. There's such a gentle vibe between the two that a fan is quoted saying, "...they give the impression that they've been married for years." (quote from the Fruits Basket Fanbook -Cat-). There's really no better way of explaining the cute relationship the two have. Because Tohru has late shifts, Yuki is always waiting for her outside and the two walk home together every time. Likewise, Tohru is one of the only people who know about Yuki's "secret base".
Before they ended up in highschool together, the two did have a chance encounter. There was a time when Tohru lost her way home when she was a little girl. Yuki, wearing Kyo's hat, had left the Sohma estate after nearly losing the will to live. Seeing Kyoko crying for her lost daughter, Yuki goes off in search for Tohru. In a small alley, he finds her, crying and balled up. In the end, he leads her back to her mother and loses the hat. After all the years between, Tohru still keeps that hat as a treasure to the reliable prince that lead her back home. She doesn't know (yet) that it was Yuki who lead her there, nor does he know that in a way, he was her first love.
There are times when Yuki acts charming around Tohru, almost as if he really likes her. Though it is true that Yuki does love her, it's revealed in chapters 83-86 that he was actually looking for the unconditional love that a mother would give. At first, he denies himself of that, and instead persuades himself that he's actually in love with her. However, as he slowly opens up to Kakeru, Yuki confronts how he really feels for her. As for Tohru, she genuinely cares for Yuki's wellbeing. She constantly looks out for him and worries over him, often becoming quite flustered whenever Yuki acts charming. So, though there is love between the two of them, it isn't romantic.
