Every living organism should be afraid of death. From a biological point of view, survival is the main goal for a organism. Sometimes survival of the species is more important than survival of the individual. But with humans the goals of life becomes more abstract. Humans are ready to die for ideas. And humans invent ideas to change the meaning of death. I believe that afterlife was partly invented because people were afraid of death. Before the religions became linear, however, there was a cyclical belief that everything repeats itself at some point so there was no clear end and therefore there was no reason to be afraid of death. And the same applies in Buddhism, where every individual is reborn after each life cycle. With Judaism, Christianity and Islam it's different because they believe that every event is unique, non-cyclical, linear. (Though they contradict this with some yearly events). They had to compensate the fear of death with an idea of a paradise. And what a better way to motivate people to behave than promise them good afterlife for good behavior. So in general for religious people death does not have the same meaning than for atheists. They can't fear death if they believe in a eternal life which is supposedly better than life as a human. And to end, I will answer the question directly. Yes, I am terrified by the idea of my own death. I would never shorten my own life or take my own life. Whatever emotions humans feel, be it utter sadness or feeling of uselessness, it is still better than to cease to exist. But I do not think about death because there is nothing I can do to stop it. So worrying about it is kind of pointless. So in that way the irrationality of worrying about the inevitable beats fear.