People Katara knows, good and bad
This is by no means close to done yet, since Katara has a tendency to try and talk to/find ground with most people on the ship, but here are a few of the faces she's met, some she's liked and some she hasn't so much. As predictable, family members come first.
Sokka
By far, one of the more complex relationships, if only because of the fact that they're brother and sister. One of their main differences between these two is their reaction to the ship: while Sokka was alienated and still adjusting, Katara was the first to go around and introduce herself. Another big difference between them is how they felt about learning new things: Katara through herself into it, and as a result has changed a bit from the sister Sokka knows and loves. They fight about this more than anything, but in all truth, Katara cares about Sokka more than anyone on the ship, and though she believes she has the right to adapt her ways, will still listen to Sokka and occasionally come to him for advice. If she had to be stuck on Stacy, the only thing that didn't completely freak her out was knowing her brother Sokka is always there. Where they don't always agree, she will always value his opinion and cares about what he thinks.
Family
Zuko
With all they had gone through to save their world, Katara was happy to see Zuko again: unfortunately he only had memories up to going to find Aang after defying his father. This led to a rather awkward relationship, as Katara considers Zuko a good friend despite him not remembering it. She still considers him family though, and would help him out in any way that he needs.
Toph
Their relationship is not so much strained as it is just them missing each other. Toph is still Katara's number one girlfriend and they share a room, they just haven't been able to spend a lot of time together due to GLADOS frequently throwing Toph in and out of the mix. She is overjoyed Toph has the ability to SEE better now, and her door is always open for the girl that's like her sister now.
Mai
A bit of a harder fit than the others as the two girls hardly know each other, and Mai's attitude tends to mystify Katara most of the time. Despite this, Katara has come to Mai wanting advice from time to time, and is happy she and Zuko are together on the ship.
Family aboard Stacy
Carol Davers aka Ms. Marvel
A woman Katara happened to talk to a few times that became someone she sought out for advice, and to assure on her own. In time, the two shared a bond that Katara could only see as mother/daughter, a relationship Carol herself cannot have on her own. Katara and Carol don't always get to see each other as much as they would like, but there is nothing but love and affection between the two, and Katara looks up to her.
Luna Lovegood
Deserves special mention as one of the first friends Katara made on the ship, and someone that always manages to surprise her every time they meet. Katara is fascinated with her world of magic and spells, and is always curious at learning more about the wizard that is Luna. She might never have said it, but Luna is someone she cares for deeply as a friend, and will fight anyone who tries to hurt the girl.
Arha
Once her sister in the same sisterhood, with the loss of her teacher Arha became her new one, a task both of them had to adjust to. Katara understands Arha's need to learn the ways of the Jedi, as they parallel with her own struggle to learn the ways of the Bene Gesserit, and compensated by learning her Bene Gesserit classes through Arha's Sensorium curriculum. Arha's nature is nurturing and compels Katara to trust her and try not to cause her trouble, but she also sees Arha as both guide and wanderer, someone like her still trying to learn more about herself and her body.
Negi Springfield
Katara happens to meet this experienced young ten year old wizard, and their bond happened almost immediately. She sees his innocence and his general benign nature contrasted with the dangerous spells and equally dangerous women he surrounds himself with. Because she's seen Negi learn things the hard way, she prefers approaching Negi with encouraging words and hugs. Katara treats Negi like a younger brother to the point that they share a bed, Katara recreating the closeness he had with his sister, Negi calls Katara his oneesama, a title Katara takes seriously. She sees Negi as almost a younger Aang, with the balance of innocence and the dedication to duty in tandem. She's seen his tragic past, and he's seen hers, so its also a bond of mutual duty of saving others they share.
Nura Nal-Dox
They've met only very recently, but Katara feels like she's family already in her own way. They got along swimmingly on their first outing, and so it looks like this is the beginning of having another sister in tow.
The Others on Trans 9
The anti-Yeerk prisoners: Xander, Ronan, Leela and Bella
No, Katara had no idea there was quite a few people out to take out the Yeerk, and though she isn't happy about trying to kill it now, the experience made her stronger, and had her meet the people who tried to help the crew in their own way. Some of them she still sees: she cares for Xander, Ronan is helping to train her in hand to hand combat, and she respects Bella's role as a Garou. She'd never tell anyone, but she's loyal to all of these people and would help them if they needed it.
Leon
Another person she met due to the Yeerk fiasco, on the opposing side. The ship's Chief of Security is a person that conflicts with Katara's initial reactions. She respects him and what he does, but doesn't agree with his policy on restricting teenagers from Security. Her feelings are more or less conflicted there, but she's open to finds out more about him.
Julian aka Hellion
The leader of the groups they were initially placed. She sees Julian as something of a hard person to place: handsome and headstrong, but a little reckless and not as mindful with the women he dates (or so she's heard). She gets along with him still, and can tell he wants her to stay out of trouble.
Jamie McCrimmon
One of her closest guy friends, and someone she gets into odds with at the same time. Jamie's stories about different universes and adventures with The Doctor fascinate Katara, but his dated ideas of men and women can irritate Katara enough that they have squabbled about it before. These two can't stay mad at each other for very long though, and reconcile as quickly as they fight. In another scenario, Katara would likely be dating Jamie, but for now, he two are pining for people not on the ship yet.
Luke Skywalker
She's only met him a few times, but they've all been fairly memorable. Katara knows Luke as a part of a different sect of wise people called Jedi, and is particularly trusted by Arha, so he can do no wrong. In the conversations she's had with Luke, she's seen him to be well balanced in his order, and knowledgeable in the ways of the Force.
Ben Skywalker
While she doesn't agree with his distrustful nature, she sees him as a well informed boy and aspiring to become stronger in his father's dedication to the Force. She respects him to a point and is anxious to see what he does on the ship.
Nanoha, Fate and Vivio
The first of three Katara met was Nanoha, and has seen Nanoha and Fate fight in a training session before. She respects and general likes both of the two women, and is even more amazed at the relationship they maintain despite having positions on the ship. To her, its an example of a relationship she wants to be in, where two people share their burdens and troubles together. Vivio, she sees, is an example of what happens when two good people raise a child as strong as they are, and is never not charmed by the little girl.
Will and Matt
Katara met Will first where she explained about how she was a hero in her world, one with elements in their own way. She became a quick friend of Will's, and would listen with attention when Will talked about her boyfriend Matt. When said boyfriend actually appeared on the ship, he and Katara bonded right away, and Katara was overjoyed to see Will so happy. Outside of Will, Katara likes Matt's easygoing nature and her opinion of him improved when he introduced her to the W.I.T.C.H. bus, a place she goes to train and meditate now. With his demeanor, the playing of a mean guitar and sweet voice, Katara has sported a crush on the boy, one she herself isn't aware of and will very likely continue.
Irma
Another member of W.I.T.C.H., Irma's power is linked with water, so it was only natural that she and Katara would meet and get along (also, Katara uses her room on the bus). While they don't get to meet as much as Katara would like, she still treats her like a friend and will give advice if asked.
Aeneas
A strange blue alien that shares Katara's manipulation of water, she gravitates toward him and is curious about where he's from and what he's done. She is also compelled to be affectionate with him too, hugging and stroking his fur, like she feels he's had something hurt him and wants it to go away. She so also very playful with Aeneas and laughs at his pranks. she cares for him.
Mulan
A foreigner to Katara when they first met, they nonetheless share a bond as young women trying to better themselves in their prospective arts. Katara has been teaching her meditation to ground her in times and strife, and Mulan has shared tales with her about a strange place called China that she listens to eagerly.
Team Renne: Renne, Billy Cranston and Goliath
The team also includes Jamie McCrimmon but as she knew him fairly well before this, is not listed here. Katara followed Jamie and Billy into the Sensorium one day only to find the weakened mindscape of then unknown life form to her, Renne. Finding out Renne and Billy were linked in a way that if Renne died Billy did too, Katara with the others helped give Billy the strength to penetrate through to Renne and help him. After this experience, Katara sought Billy and Renne as friends, and will try to find Goliath whenever she can. With Billy, Katara sees what he lacks in physical strength doubled over in intelligence and strength as a tactician. She is helping him train to get better at the moment, and he in turns tells her about the things in other worlds she knows nothing about. Renne is an enigma Katara is both affectionate and in awe of, much like Aeneas, and she longs to find out what Renne truly is.
Allen
She still doesn't quite now how to place Allen as far as her friends. She sees him from time to time, and he's pretty smart though, so she's sure she'll figure that out eventually.
Sasami
She's just met her and so far she likes the spunky little girl. She seems to be one that's stolen Negi's affections, and is impressed by how compassionate Sasami is about helping others.
Rhiow
A cat (which still surprises Katara) who has an extensive knowledge of magic and commands respect. While Katara pets and strokes Rhiow like a normal cat, she also trusts in Rhiow's feel of things and commanding nature. Like Arha, Rhiow is someone that demands focus and dedication, much like any other teacher, and is yet again another character that Katara associates with the mystery of magic.
Sofia
A girl that Katara is only starting to get to know, specifically from the Nightmare King plot. She finds her interesting, and has head her name connected to Ben 10's for some reason.
Kate Bishop
Someone Katara's met a couple of times, most notably when she was playing an instrument. Katara would like to get to know her a little more.
Kaylee Fry
A girl who's enthusiasm even she can't compete with. A girl Katara senses as a truly benign soul.
Danny Phantom
An occasional friend if Katara's, he also stopped her from going after he Yeerk, so she has his mutual respect.
Ben 10
A recent friend of Katara's, he's a member of the Outsiders, a team Katara is trying to get back started up, and is a relatively nice guy. He;s also romantically involved (or not) with Irma, which piques Katara's interest.
Nanashi
A vampire Katara met and is going to be training with. While she has some good qualities, Nanashi is predisposed to violence and is very strict with Negi, things Katara does not approve of. What will happen with them later is anyone's guess.
Cargn aka The Seer
He is the man who was responsible for holding back the Nightmare King, and by association, a man who knows who she is but Katara is unaware of this. Because he is the direct link to the fight with the Ohm, Katara goes to seek council and advice from him where she can get it. She wants to stop the Ohm in any way she can, so chances are they'll be interacting more in the future.
Others
Lex Luthor
While he never directly hurt any of Katara's friends, Lex Luthor's negligence cost them time and tension in the group. Katara got a bit of this when she defended him, preferring to get information from him about the enemies they were facing rather than going blind. This earned her the cold shoulder from those in the group. Katara can talk to Lex and sees him as Azula in his own way, minus the malice and preference of violence, she just can't trust him fully.
Asuka Langley Soryu
Yeah, these two were bound to not get along. Katara is motherly, enthusiastic and idealistic while Asuka is brash, arrogant and condescending. They don't like each other.
Paco
Due to the Lex Luthor fiasco and losing an arm, Paco opted to not speak to anyone defending Lex, including Katara. She regrets that, but still believed she did what she did out of fear of any one else getting hurt, not to take sides.
Brainy Bot
The epitome of what it means to be a true superhero. Katara never forgot losing Brainy, and still shines the statue of him in the Outsider's headquarters as a memorial. She still misses him, and hopes that the crew will never have to lose someone like that again.
Gone, but not truly forgotten...
Teacher.
Good friend.
Aang, the Avatar, the Last Airbender and the love of her life.