I've never been a fan of love triangles. Most of them end messily and add a level of depression to a story. I didn't mind this one as much though, because I thought it was handled beautifully. Yuki and Tohru were never truly themselves around each other. Without even knowing it, Tohru played the role of Yuki's mother and caretaker the moment she stepped between Yuki and Akito. She has always viewed Yuki based on his reputation of a prince, and fell into the friend/mother role very easily. Kyo and Tohru are always themselves around each other, and they can tell when the other is upset. This is never really true of Yuki and Tohru's relationship. They are there for each other, but Yuki doesn't realize when Tohru is acting, and Yuki doesn't always act like himself around Tohru. Kyo has been himself, and Tohru had already developed feelings for him before she even met him (as a number one year of the cat fan). But more importantly, Tohru understands Kyo, and she is able to treat him like a person, unlike any of the other members of the zodiac. In the same way, Kyo understands Tohru and doesn't put her on a pedestal like the other members of the zodiac do.
Most of the love triangle issues that happen in stories have to do with the type of characters the main character is interested in. In Fruits Basket, I found that it wasn't about the type of person, but how well Tohru knew them.
In the story, Yuki picks up on Tohru's feelings for Kyo and Kyo's feelings for Tohru long before either of them realize it. He has an interesting time being a third wheel and reflects on it with a new friend he makes at the time. This one observation that Yuki makes helps him understand that he doesn't view Tohru the same way Kyo views her, and although it is a painful experience, he is eventually able to find someone he truly cares for.
Many readers argue that Machi is Yuki's replacement for Tohru, but I see no evidence of this in the story. Yuki doesn't act like he does around Tohru when he meets Machi, and Machi is the first person to recognize and appreciate Yuki's flaws. Even in Tohru's eyes Yuki seemed perfect and prince like, but she never recognized when he was acting, and she never seemed to question the reputation that people gave Yuki at school. Machi does. Machi calls out Yuki on his faults, and while everyone gets mad at her, Yuki appreciates it. This is how Machi treats Yuki like a person, and not like the school boy idol that his fangirls in High School make him out to be. Yuki sees Machi as a person too. He recognizes that Machi has certain habits, and he learns that Machi acts a certain way when she likes something or someone. He makes an effort to be a part of Machi's life, and he helps her recognize her own value.
Normally love triangles leave the third wheel lost, confused, hurt and a little jaded. Fruits Basket showed the other side of that story, how Yuki overcame an unrequited crush and discovered that he could find someone who cared for him the way he thought he cared for Tohru. Once he discovers that Machi likes him, Yuki is finally able to tell Tohru that he viewed her as his mother, which she takes as the highest compliment.
I won't say that this love triangle worked out smoothly, for it was a bumpy ride for all three characters, but it seemed reasonable and it didn't feel incomplete.
Kyo and Tohru belong together just as much as Yuki and Machi belong together.