Listed in chronological order:

On the Forest Owls' train, before the train mission
Rinoa: Oh yeah, my name's Rinoa. Very pleased to meet you, Squall. SeeD members dance quite well, don't they?
Squall: Approach your target inconspicuously at a dance party... There may be missions requiring this sort of subterfuge. It's expected of SeeD to learn various skills.
Rinoa: Ohhh... So it's work related. That's too bad...

Outside the Timber communications tower
Rinoa: How sad... Act on my decision? That's our duty? Oh, what an easy life it must be, just to follow orders...
Squall: Call it what you want. All we want is for you to achieve your goal using our help. I find it hard to believe that you can do it, though...
Rinoa: W-What did you say!? If you have something to say, just say it!

Discussing Seifer's fate after his "arrest"
Squall: He may already be dead.
Rinoa: How can you be so casual? I feel... sorry for him.
Squall: (... Feel sorry? Seifer would hate to hear that.) *laughs*
Rinoa: What's so funny!? You're terrible!

Following a harsh comment to Zell made by Squall
Rinoa: Oh, you're just a great leader, aren't you... Do you actually have fun acting so callous towards your comrades?
Squall: (... Not again.)
Rinoa: Zell wants your support.
Squall: (I knew it was gonna be something like that...)
Rinoa: Any kind of encouragement will make...
Squall: (That's just to ease your mind. Am I the only one who thinks that? No, I'm sure Seifer...)
Rinoa: Don't you ever worry about or even think about the well-being of your comrades!?
Squall: (I don't believe in relying on others.)
Rinoa: Don't you understand!?
Squall: (... Whatever.)

Waiting for General Caraway inside his house
Rinoa: Hmph... He always does this! So discourteous... making people wait. I'm gonna go complain. Everyone just wait here. Oh, by the way, this is my house. So don't worry. Umm, just don't leave me here, ok?
Squall: Is something going to happen to you?
Rinoa: Umm... I don't know. Just treat this like an order from your client, ok?

After Irvine and Squall rescued Rinoa from the Iguions
Rinoa: I was scared... Really scared.
Squall: It's over now.
Rinoa: I was scared... I was really, really scared.
Squall: You're used to battles, aren't you?
Rinoa: I couldn't... I just couldn't. I couldn't fight alone...
Squall: (... You're not ready for all of this.) Better get going. I haven't forgot your order. Just stay close to me.

While Balamb Garden is drifting in the ocean
Rinoa: Hey. You looked so adorable, sleeping like a baby. Come on, get up. Let's go.
Squall: Go where?
Rinoa: Give me a tour of the Garden.
Squall: ... Is this another one of your orders?
Rinoa: No. I just want you to show me around. You know, to get acquainted with the place. Please?
Squall: ... Fine.

Following the encounter with the White SeeD
Rinoa: Hey, again.
Squall: I wasn't asleep.
Rinoa: Oh really? I think I heard you talking in your sleep. I'm not telling you what you said. Hey, let's go for a walk.
Squall: Again?
Rinoa: That was a guided tour! This time, it's a walk.
Squall: Just go by yourself. It's safe here.
Rinoa: It's not that I want a guard with me. You know... You're always too deep in thought. Why don't you lighten up a little? It's not good to think much. What I'm trying to say is... It would be my honor... to have your company, your highness, in hopes that I may get your mind off things. How about it, your highness?
Squall: Fine.
Rinoa: Thank you, your highness! Alright, let's get goin'!

During the concert arranged in Squall's honor
Rinoa: Squall, I'm sure there'll be a lot of difficult things that you'll have to deal with from now on. We were talking about that, and saying how you'll probably try to handle everything on your own.
Squall: (I probably will.)
Rinoa: They know you too well. I do, too, although I haven't been around you that long. Y'know, when you start thinking, you tend to frown like this. *mimics Squall's pose*
Squall: I'm out of here.
Rinoa: Oh come on! I'm sorry! But really, we were saying that... well... You can't handle everything on your own. *shoves Squall*
Squall: !!!
Rinoa: That's it! Just let out anything! Anything... We want you to talk to us a little more. That's all. Y'know, if there's anything you want to tell us, or anything we can do, don't hesitate to let us know. I know it's not easy but I wish you would trust us and rely on us a little more.
Squall: (Am I that untrusting...? Maybe I'm this way because I'm scared. Nothing lasts in this world. It feels great to have friends who believe in you, and adults you can rely on. That's why it's so dangerous, especially if you become used to it. Someday you're bound to lose everything. Everybody around you will be gone. Then what are you left with? Nothing. Nobody... It's so miserable. And it's inevitable. It's so hard to recover from something like that. I never ever want to deal with that again. I can't even if it means being alone...)

After Squall rescues Rinoa during the battle with Galbadia Garden
Rinoa: Squall! Thank you.
Squall: It was, ah... don't worry about it. It was my job. We're still under contract. And it was everybody else's idea, too. And I just happened to find you. That's all. So like I said, don't worry about it.
Rinoa: You know something, I couldn't afford to fall off that cliff and die. I have something very important that belongs to you. I can't die until I give it back to you, right? Zell gave it to me, see? I've been holding onto it.
Squall: (I'm gonna kill him...) That's my favorite ring. You'd better give it back.
Rinoa: I'm sure it is. It's a cool-looking ring. What's this monster on it anyway?
Squall: It's not a monster. It's a lion. Lions are known for their great strength and pride.
Rinoa: Hmm... great strength... pride... Kinda like you, Squall.
Squall: I wish...
Rinoa: Hmm... so this L I O N of yours, does it have a name?
Squall: Of course. Griever.
Rinoa: So that's what you call it. You know Zell said he'll make me one exactly like it. Who knows, maybe I can become like a lion, too. That'd be crazy, huh!? I mean, everyone might, y'know, get the wrong idea about us.
Squall: (If it's so crazy, why do you sound so delighted? Everyone is trying to get us together. It's so obvious even I can tell.) You sound like you want everyone to get the wrong idea.
Rinoa: No-no-no-no-no!

Following the second battle with Edea, where Rinoa was put into a coma
Squall: (Rinoa... You feel so cold. Are you going to be like this forever?) ...... Isn't there anything I can do!? You were so full of life. Now you don't even make a sound... I want to hear your voice. (This is like talking to a wall.) Rinoa... Call my name. (......)

Speaking through Ellone after Ultimecia possessed Rinoa and used her to open Adel's seal
Rinoa: (Good bye. Squall...)
Squall: (Rinoa!!! No!!! Don't give up!!!)
Rinoa: (......?)
Squall: (Can you hear me!? It's Squall... Rinoa!!! Rinoa!!! Rinoa, come on! Try to remember! Rinoa! I'm right there with you! Listen to me!)
Rinoa: (I'm... still......... alive? Squall...?)

Immediately after boarding the Ragnarok, following the space rescue
Rinoa: Give me a hug.
Squall: (...?)
Rinoa: A real tight one! I need to know that I'm alive!
Squall: (...Alive? We still have to get back.) We may be alive right now... But look at our situation... You want to live, right? You want to go back and see everyone, right?
Rinoa: And not become other people's memories?
Squall: That's right.

In the cockpit of the Ragnarok, heading back from space
Rinoa: We'll be home soon?
Squall: Hopefully. Now go sit down.
Rinoa: Just a little longer.
Squall: Why are you holding onto me like this?
Rinoa: You don't like this, Squall?
Squall: Just not used to it.
Rinoa: How about when you were little? Didn't you feel safe and secure being held by your parents?
Squall: I can't remember anything about my parents... But... Ellone was there for me. Ellone was there to hold my hand.
Rinoa: Make you feel safe and secure?
Squall: Sure. But she left. Just disappeared. I'm afraid... Afraid of having that feeling of comfort taken away.
Rinoa: You were afraid of losing us? Is that why you kept your distance?
Squall: I was always alone...
Rinoa: Squall... You missed out on all the good things in life. You've missed out on so much.
Squall: ... Maybe.
Rinoa: Definitely. I like it like this. I liked having my mom hold me. My dad, too, back when we got along.
Squall: I'm not your mom.
Rinoa: No, of course not. But now... Squall, you're the one who gives me the most comfort. Comfort and happiness... And annoyance and disappointment, too!
Squall: ... Whatever.
Rinoa: Whatever.
Squall: You should get back to your seat now.
Rinoa: Just a little longer.
Squall: (You'll be safer in your seat.)
Rinoa: We're gonna make it home, right?
Squall: We can only hope.
Rinoa: When we get back... We won't be able to stay together, huh?
Squall: ... Maybe. No one can predict the future, there are no guarantees. Those were your words, Rinoa.
Rinoa: That's not what I meant.
Squall: We'll figure out what to do once we get back.

After landing, before Rinoa is taken to the sorceress memorial
Squall: Rinoa! Don't go!
Rinoa: ...... Thanks, Squall. But I have to go...
Squall: (...... Rinoa.)
Rinoa: ...... Oh... I still have your ring.
Squall: You keep it.
Rinoa: You sure?
Squall: Yeah.

In the flower field behind the orphanage, before the final confrontation
Squall: Don't worry about it. There've been many good sorceress. Edea was one. You can be like her.
Rinoa: But Edea's still... I can't guarantee anything, either, if Ultimecia possesses me again... You saw me. She controlled me in outer space and made me break Adel's seal. What might happen next time? What will I end up doing? Will I end up fighting everyone? ... Scary thought, isn't it?
Squall: (Rinoa...... Even if you end up as the world's enemy. I'll... I'll be your knight.)
Rinoa: If I fall under Ultimecia's control again... SeeD will come kill me, right? And the leader of SeeD is you, Squall... Squall's sword will pierce my heart...... I guess it's ok if it's you, Squall. Nobody else. Squall, if that ever happens...
Squall: That's enough! I'll never do anything like that. The sorceress I'm after is not you, Rinoa. My enemy is the sorceress from the future... Ultimecia.
Rinoa: Ultimecia lives in the future and possesses me. She uses my body as her extension in this world. How will you save me?
Squall: I'll come up with something... There's gotta be a way.
Rinoa: ......
Squall: Don't worry. Trust me.
Rinoa: ... I trust you. Well, until you find a way, maybe... Maybe I should stay in Esthar, at that memorial? Wouldn't that be better?
Squall: No... That'd be pointless. I'll just end up going after you again. Rinoa... Just stay close to me.
Rinoa: Oh... Those words!
Squall: What?
Rinoa: That's what started everything.
Squall: What are you talking about?
Rinoa: You don't remember?
Squall: Something I said?
Rinoa: Oh, just forget it!
Squall: No, its because of the GF. That's why I forgot.
Rinoa: That's just an excuse.
Squall: Feeling better?
Rinoa: Yeah. Can I tell you a story? I had a dream. It was a scary dream. We make a promise. We promise to see shooting stars together. I get dressed up and put on your ring. But the thing is, I can't remember where I'm supposed to meet you. I started to panic. I really want to see you, Squall, but I don't know where to go. I start running through the mountains, the desert, the plains... Through Timber, Balamb, and Galbadia... When I realized I can't run any longer... I... I just want to see you so badly... So I scream, Squall, where are you!? Then I woke up. I was crying. I'm sorry. You don't have to say anything. I just felt like I had to tell you.
Squall: It was just a dream... It doesn't mean anything. Don't worry about it.
Rinoa: ... I guess you're right.
Squall: How about this... I'll be here...
Rinoa: ... Why?
Squall: The reason why you couldn't find me was because we haven't promised yet.
Rinoa: Promised...?
Squall: I'll be waiting for you. If you come here, you'll find me. I promise.
Rinoa: I'll be here, too. It's a promise! Thanks, Squall! Next time, we'll meet for sure!

While heading to the source of all the problems
Rinoa: I'll... probably disappear...
Squall: Just stay by my side. I won't let you disappear!!!