Below are quotes from Volume 1.

Note: These quotes were taken by me. I spent time actually going through the Volumes and picking out good quotes (sad, I know, lol). Please get my permission to use them or I'll get Kyou to use you as a scratching post. ^^

Yuki: The Cat is a fool. And he has a bad nature.
Tohru: Huh?
Yuki: Did you know......that the Chinese Zodiac is actually a time keeping system of tens and twelves? It was used for calendars and clocks. Later, astrologers combined it with the principles of Yin and Yang, the five elements and symmetry in order to tell fortunes.
Tohru: Animals had nothing to do with it?
Yuki: No. When and why they added the animals............no one really knows. But there was never room for the Cat in the Chinese Zodiac. And it's better that way. The Cat would throw off everything. The Cat really is a fool.

Tohru (thinks):I meant it. I really was crying. When God and the twelve animals were enjoying the banquet on the far off mountain......the Cat was dreaming of a banquet the next day that would never happen. Poor thing-sleeping soundly unaware of the deceit.

Tohru (to Kyou): I mean, I'd never be mad at you. How could I be? I love you. I've always loved the Cat from the Zodiac!
Kyou: Huh?
Tohru: It's true. I......I wanted to be born in the Year Of The Cat. I mean, um, I......I want to be friends.
Kyou (remembers what Shigure said): "And if someone did, what would you do?" "If a girl told you......she loved you." *Kyou blushes, eyes wide*
Kyou: .........!! That's stu--! It's not that great. Being a Cat.

Yuki (to Tohru, while in Rat form): When I was at the main house......it felt like I was in a cage, always being watched by the family and Akito. I always wanted to have a "normal" life, surrounded by "normal" people. So I applied to a co-ed school and left home. But I couldn't get out of the cage after all. I just wound up in another Sohma house. And I still can't associate with "normal" people. I don't mean to turn them away. But some part of me can't deal with other people. I cut myself off from other people......because I'm afraid of getting hurt. And......because I'm like this. (thinks) The hesitation and the fear won't go away. (says) But Kyou is different. He might be extremely shy......but if he gets used to being around people, I think he's the type that attracts others…that has many friends. Even if he can't join the zodiac......he might be able to interact with normal people and have a normal life. That's why...(thinks) ...I've always......wished I could be like that too. (says) That's why I get annoyed......when I look at Kyou, who wants to be a Sohma.

Tohru (thinks):I made......a mistake. I was never going to be more than......a temporary guest......but I made the mistake......of thinking of them......as my family.

(Tohru has just left the Sohma's house to go to and live in her grandfather's house.)
Shigure (to Yuki): I thought you'd stop her.
Yuki: Why? We knew it was only until the remodelling was finished.
Kyou: Eh. It's better this way. It's not right for an outsider to be here......anyway.
Shigure: .....(thinks) So why does it feel like a funeral home in here?

(Yuki and Kyou have just got Tohru from her Grandfather's house.)
Kyou: I don't know why the hell I'm doing this. Why did I get all irritated the moment you left? It didn't make any sense, so I got even more annoyed!
Tohru (thinks):Even though......they fought......they came......to get me?
Kyou: Anyway...if you didn't really want to leave......you should have said so in the first place!
Tohru: EH?! But-How did you--?
Kyou: I heard you.
Tohru (blushing): .....
Kyou: ....I thought that you......were all about saying what you feel. Normally I hate people who whine all the time......but in your case......it would be okay......to complain...be selfish...say what you want...once in a while. It's okay......to let yourself be sad.