I mentioned this one before but it still stands out for me:
Season 5 Episode 16 - The Body
***
Anya: Are they gonna cut the body open?
Willow: Oh my god. Would you just... stop talking? Just... shut your mouth. Please.
Anya: What am I doing?
Willow: How can you act like that?
Anya: Am I supposed to be changing my clothes a lot? Is that the helpful thing to do?
Xander: Guys...
Willow: The way you behave.
Anya: Nobody will tell me.
Willow: Because it's not okay for you to be asking these things.
Anya: But I don't understand.
[begins to cry]
Anya: I don't understand how this all happens. How we go through this. I mean, I knew her, and then she's- There's just a body, and I don't understand why she just can't get back in it and not be dead anymore. It's stupid. It's mortal and stupid. And-and Xander's crying and not talking, and-and I was having fruit punch, and I thought, well, Joyce will never have any more fruit punch ever, and she'll never have eggs, or yawn or brush her hair, not ever, and no one will explain to me why.
***
I just fall apart during this scene every stinking time I see it.
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As for funny things, I had to give it some thought and although it wasn't a blooper I loved Anya's total fear of bunnies, especially when she dressed up as one for Halloween and said it was the scariest thing she could think of. I loved Anya.