Unlike for Mulder and Scully there aren't many quotes for Buffy and Giles -more looks and gestures actually. Nevertheless I selected a few quotes that show the depth of the relationship between Buffy and Giles and also added the lyrics from Goodbye To You (the song that was played by Michelle Branch in the Bronze while we see Giles leaving and Buffy sitting very depressed and sad in the Bronze listening to that song).

GILES:  I've made up my mind.
BUFFY:  So have I.
GILES:  I made up my mine first! I'm older and wiser than you, and just... just do what you're told for once! Alright?

BUFFY:  That's not how it goes. I'm the Slayer.
BUFFY:  I know.
[She pretends to turn to go, but then throws a hard punch to his face, knocking him out. He falls backward to the floor. Ms. Calendar scrambles to his aid. Buffy sees her cross on the table and puts it back on. Ms. Calendar lifts Giles' head in her hands and gets under it with her knees. She looks up at Buffy. ]
BUFFY:  When he wakes up tell him... I don't know. Think of something cool, tell him I said it.
[Prophecy Girl]

GILES to BUFFY : …The coming months a-are gonna, are gonna be hard... I, I suspect on all of us, but... if it's guilt you're looking for, Buffy, I'm, I'm not your man. All you will get from me is, is my support. And my respect.
[Innocence]

GILES: Why did you come here?! This wasn't your fight!
[She punches him in the jaw, and he spins and falls to the pavement.]
BUFFY: Are you trying to get yourself killed?!
[She begins to cry and crouches down to hug him. He cries and hugs her back. ]
BUFFY: You can't leave me. I can't do this alone.
[Passion]

Giles: [imploringly] You have to listen to me. Because I've told you this, the test is invalidated. You will be safe now, I promise you. Now, whatever I have to do to deal with Kralik... and to win back your trust...

Quentin: Your affection for your charge has rendered you incapable of clear and impartial judgment. [Buffy looks at Giles] You have a father's love for the child, and that is useless to the cause. [Giles looks down]
[Helpless]

GILES: Buffy, calm down. The scandal here is not anything you've done wrong, it's the way they're behaving. Holding what they know hostage with a gun pointed at my bleeding green card, no less. [sighs] It's humiliating.
BUFFY: Also smart. They picked the perfect thing. I can't lose you.
GILES: [softly] Thank you.
[Checkpoint]

GILES: I'm so proud of you. You've come so far. You're everything a Watcher ... everything I could have hoped for.
[Spiral]

GILES: [smiling] Oh God, Buffy.
[He hugs her. She hugs him back, closes her eyes.]
GILES: You're alive. You're here. And you're still ... [strained] ...remarkably strong.
BUFFY: Huh? Oh. [lets him go] Sorry.
GILES: Willow told me, but I didn't really let myself believe ...
BUFFY: I take a little getting used to. I'm still getting used to me.
GILES: It's, uh ... you're ...
BUFFY: A miracle?
GILES: Yes. But then, I always thought so.
[Flooded]

Song: “Wish I could Stay”
[Giles emerges from the back, overlaps with Tara's last word]
GILES: Believe me, I don't wanna go
GILES/TARA: And it'll grieve me 'cause I love you so
[shot of Willow and Buffy talking, oblivious to the singing]
[Once More With Feeling]

GILES: You have to be strong. I'm, I'm trying to…
BUFFY: [jumps up] Trying to, to what? [angrily] Desert me? Abandon me? Leave me all alone when I really need somebody?
GILES: [quietly] I don't want to leave…
BUFFY: So don't. Please don't.
[Tabula Rasa]

BUFFY: [sighs, looks around] You know, I didn't even realize it was December.
Maybe when we get home, we should decorate the rubble. [looks at Giles]
Think you'll ever show up for a real visit? The kind where the world isn't about to end?
GILES: If we survive this, I promise.
BUFFY: Good. 'Cause I miss you.
GILES: I miss you too.
[Bring On The Night]

Goodbye To You

Of all the things I believed in
I just wanna get it over with
Tears warm behind my eyes, but I do not cry
Counting the days that pass me by
I've been searchin' deep down in my soul
Words that I'm hearin' are starting to get old
Feels like I'm starting all over again
The last three years were just pretend
And I said...

Goodbye to you
Goodbye to everything
That I knew
You were the one I loved
The one thing that I tried to hold on to

I used to get lost in your eyes
And it seems that I can't live a day without you
Closin' my eyes, you chase my thoughts away
To a place where I am blinded by the light
But it's not right

Goodbye to you
Goodbye to everything
That I knew
You were the one I loved
The one thing that I tried to hold on to

And it hurts to want
Everything and nothing at the same time
I want what's yours and I
Want what's mine
I want you
But I'm not giving in this time

Goodbye to you
Goodbye to everything
That I knew
You were the one I loved
The one thing that I tried to hold on to

If You know anymore quotes that are in your opinion very UST than tell me!