Kilgore: I love the smell of napalm in the morning.
Willard: Hey soldier, do you know who's in command here?
Soldier: Ain't you?
Chef: Why do all you guys sit on your helmets?
Soldier: So we don't get our balls blown off.
Kilgore: What the hell do you know about surfing, Major? You're from goddamned New Jersey!
Willard: Everyone gets everything he wants. I wanted a mission, and for my sins, they gave me one. Brought it up to me like room service. It was a real choice mission, and when it was over, I never wanted another.
Kilgore: Charlie don't surf!
Kilgore: You either surf or you fight.
Lance: Disneyland. Fuck, man, this is better than Disneyland.
Willard: If that's how Kilgore fought the war I began to wonder what they really had against Kurtz. It wasn't just insanity and murder, there was enough of that to go around for everyone.
Kurtz: We must kill them. We must incinerate them. Pig after pig. Cow after cow. Village after village. Army after army.
Kurtz: The horror... The horror.
Answer: It's not any specific song; it's just the kind of generic piano music you'd hear at dinner at a high-class restaurant of the era. Think of scenes in movies, films, etc. set or made in the '50s and '60s, where the characters go to a nice dinner and there's someone at the piano playing unobtrusive music to accompany the food/conversation.