Kurtz dies murmuring these words:

KURTZ: The horror…the horror… 

It's his version of saying, "Seacrest out."

But what is "the horror," other than a quotation from Heart of Darkness? It could be Kurtz's final assessment of his own actions and what he's seen, the horror of war and the horror of what people are capable of doing to others. It could be a commentary on human nature in general. He could be talking about Jake and Vienna or Plan 9 from Outer Space. It's meant to be ambiguous. Regardless, Kurtz didn't die happy.