Essence of Bangel: Heartbreaking-Sewer-Talk Buffy & Angel
In "The Prom" episode, Angel is trying to break up with Buffy during their patrol of the sewer, and a vampire makes the mistake of interrupting them.

Angel (to Buffy): "Come on, don't be that way."
A vampire drops from the roof, growling.
Buffy (to the vampire, dusting him with ease): "Not now."

To me, this is the epitome of Buffy's relationship with Angel: love, angst, and dusting!

Essence of the Slayer: Vision-Quest Buffy & the First Slayer
In the "Intervention" episode, Buffy goes on a quest to find out more about the nature of the Slayer. She is sitting by a camp fire in the desert, when the First Slayer appears in a vision. The First Slayer prophesies Buffy's sacrifice, but Buffy misunderstands her.

First Slayer: "Death is your gift."
Buffy: "Death ..."
First Slayer: "Is your gift."
Buffy: "Okay, no. Death is not a gift. My mother just died. I know this. If I have to kill demons because it makes the world a better place, then I kill demons, but it's not a gift to anybody."
First Slayer: "Your question has been answered."

I see this as a moment that illustrates Buffy's feelings about her role as a slayer. She does her job, but she has always questioned her use of power, unlike the way Faith approached the calling.