Some spoilers, especially toward the bottom.

Kenshin: At first, she becomes attached to him and simply doesn't want him to leave. Watsuki-sensei himself admitted he didn't know if they'd fall in love. Later, they do, as anyone with eyes (or who's followed the Revenge Arc) can tell, but I rather like that her worries over him leaving in the pre-Kyoto stories aren't centered around romantic love. They have a very cute relationship, pulling on each other's ponytails but staying fiercely protective of each other as well. In the manga, she's a bit more serenely understanding of him; in the anime, she goes through more mood swings.

Yahiko: He's her student, but their relationship is much closer to brother/sister. They insult each other, she tries to harm him, but he also worries about her and she about him. His behavior in the Revenge Arc shows that he really cares about her, and she worries over him all the time - trying to keep him from exceeding his strength in fights and so on. In the Kyoto Arc, she's devastated when she thinks he's been killed (it's JUST before Hiko's appearance).

Sano: A sort of grudging friendship. She resents his freeloading, which is understandable, since she's poor, but she likes him and respects his friendship with Kenshin. He's got sort of an older-brother fondness for her, and he likes anyone who'll pick up the tab. He thinks she's a bit too emotional, though, at least regarding Kenshin... sort of an "Eh...... chicks" attitude.

Megumi: Rivalry! Lots of it, too. Megumi's a natural flirt and a natural bitch, so once she realizes her flirting with Kenshin gets to Kaoru, she turns it up a few notches. She's not dumb, though, and can see Kenshin's not interested, and that Kaoru is the most important to him. Kaoru is less astute in this relationship; she just sees someone flirting with/trying to steal Kenshin and gets mad. If RK were a shojo manga, Kaoru would be the main character and Megumi would be the enemy-slash-Yui-figure. There are glimmers of caring there, but calling it a sisterly relationship is stretching, in my opinion. (And yes, I have a sister. We fight, but not every second we're together.) I think Watsuki either didn't know how to develop Megumi as a three-dimensional character, or just preferred to use her as a very simple, flat place-holder and devil's advocate. To be fair, I think she's a victim of the genre as much or more than Kaoru - where Kaoru is stifled and eventually transformed from a spunky fighter into a wife and mother, Megumi is just ignored and eventually moved away entirely, and her relationship with Sano (even Watsuki acknowledged they had chemistry!) was ignored and then abandoned because the story needed more room for all the fighting. She's also characterized somewhat inconsistently - the bitch who told Kaoru she'd never replace Tomoe was not, in my opinion, the same person who slapped some sense into Kaoru at the beginning of the Kyoto Arc. I like Kyoto Megumi, or the Megumi who's so much fun with Sano, but I HATE the other version. And yes, with Kyoto-departure Megumi I do see where the "sisterly" thing comes from. But it goes away later on, hence my interpretation.

Misao: They don't really get much chance to get to know each other, but they're friends. They're close in age, and they have a lot in common. Both are fighters, so they don't really get to be "normal girls," and both love men who are missing (at the time that Kaoru and Misao meet), tormented, and possibly not even interested. They bond during the Kyoto arc, but events and distance keep them from maintaining much contact after that. Put them in a shojo manga, and they'd be best friends and classmates.

Tae and Tsubame: To carry out the shojo theme, they'd be... much closer to her age. They'd also be the "other friends." Every shojo heroine has a best friend and about two others, who are presumably best friends with each other. Tae takes the older-sister role, lecturing Kaoru on how to snag Kenshin (she never takes the advice, you notice...) In the Revenge Arc Kaoru sort of adopts Tsubame, who I think would definitely benefit from having Kaoru as a role model (though she's a pretty cool little girl on her own. The anime doesn't do her justice.)

Aoshi: They barely meet. She does have some words with him in the Kyoto arc, and he seems to have respect for her, but his actions in the Revenge arc seem mostly motivated by his relations with the other people involved, mostly Misao and Kenshin. Especially Misao.

Dr. Genzai, Ayame and Suzumi: They're only in the anime, but then, I like the anime. They're sort of adoptive family. The kids are cute.... really, really, insanely cute. To the point that you may want to rip their kawaii heads from their tiny shoulders if you're in a bad mood when you watch the anime. Kenshin never feels that way. They primarily exist to show how good he is with children, and to make women everywhere melt as they realize what a wonderful father he'll be. Kaoru actually doesn't deal with them too much. Perhaps she does some melting offscreen or something.

Hiko Seijuro: Kenshin's master. If the name still doesn't ring a bell, try to call to mind Suzukaze Mayo's pained tones as she half-wails "Shisho..." and you know who I'm talking about. The tall, buff guy in the Spawn cloak. Kaoru encounters him briefly in the Kyoto arc, and interestingly, never takes offense at his constant offhand insults toward Kenshin. I think she takes them in the spirit in which they're meant, and knows that in his way he cares about Kenshin.

Saitou: Oh geez. Well, okay... I think he views her as a nice enough girl who really doesn't deserve to be caught up in Kenshin's problems... but if she insists on sticking around, it's not HIS fault she makes stupid mistakes. He has no interest in rescuing anyone just because they need it.

Enishi: You know, plenty of people like to think he's in love with her, and some think they would be a good couple and I suppose if I weren't all over the K&K thing I might agree. I can see the logic - they're relatively close in age, and it would do Enishi good to learn to deal with women who are (a) alive and (b) not related to him. This is a relationship in which most of the benefits go to Enishi. But I just don't like Enishi THAT much, and I DO like Kenshin that much, and the K&K age difference is not that huge by the standards of the time, and... yeah.