Yes, because I'll need to experience firsthand the end of my existence, and I'm helpless to prevent it. It's the crux of human existence, when we took from the tree of knowledge (figuratively or literally) we became self-aware and in doing so our mortality no longer suited us. Death should scare you. It also shouldn't scare you. Just because it's a tragic unavoidable flaw in our being doesn't mean that there's any use dwelling on it.
I think humankind could cure death. Just as we can cure many diseases, we will come to understand aging itself and devise a means to treat it. When you run out of things that can kill a person, immortality has been achieved. Future generations will look back at us and say, "can you believe people actually used to die" in the same way we look back at generations and say, "can you believe people actually used to die of this or that before penicillin?"
Unfortunately, I doubt this will come during my lifetime. As long as an individual may horde out of greed, immortality will only sabotage. As long as we lust over transient pleasures rather than take in the big picture, we're too small and unable to see past ourselves to be worth preserving. Achieving immortality is a major measure that we had truly transcended our mere animal tendencies and, until we have, it seems unlikely we will.
Well, with any luck, evolution's not done with us yet. As a reproducing organism, we already come with built in immortality, just not preserving that oh-so-precious personal existence of ours. Is there an afterlife? Perhaps, perhaps not: it is beyond mortal perception. However, even without an afterlife, death is not necessarily the end. As no molecule may be created nor destroyed, you can be sure we'll physically be a part of the universe forever. Still, you should savor life: as far as the destiny of a molecule goes, being part of something alive is fairly remarkable.
