Of dying? Only as much as the human brain tells me to be. If I'm confronted with a man with a gun saying he'll kill me, naturally I'll plead for my life. I still have things I want to achieve, like having a family. Other than that, I say when my time comes, my time comes and there's not a fig I can do about it.
Of getting old, then yes. Naturally as you age you pick up an increased number of ailments, and even though I'm only 28 today, I hate being ill.