Is it irrational to fear one’s own death?

There's a funny old remark that goes something like this: "I don't fear my own death, because it's not something that will happen in my lifetime." The Epicureans held something of this view. Death isn't something that happens to us, the argument goes, because when dead we no longer exist. As he was dying, David Hume is recorded as having remarked along these lines when someone asked him whether he feared death: no more so than I regret not having been born earlier. The time before we were born was nothing to us; the time after we die will be nothing, too. It's irrational to fear nothing. But, of course, it's not irrational to fear dying. The process that results in death is certainly something, and it's hardly irrational to fear the sorts of torments that afflict many in the course of that process. Then again, some hold that there's some sort of afterlife during which we might be subjected to indescibable horrors. If when dead we don't cease to exist, then maybe there is something to fear in it...