I fear that there is an afterlife. I'm fine with ending, but I don't want to get stuck in some religion's hell because I didn't know which one to pick.
Sociobiology suggests that religion was a result of evolution, that our brains got so smart that we realized our own mortality, and we needed something to make that not such a horrible thing to contemplate.
I think the real issue we have with ending is the same issue we have when we get to the end of a good story (novel, movie): We want to see what comes next. But I've seen plenty of stories that never have sequels, and plenty of canceled TV shows, so I cynically figure that my life is the same way.
It may also be useful to consider time as static, and that each moment that you existed has a different "you" in it, like an insect trapped in amber. Each "you" sees all the previous yous and thinks that they're part of the same being. If you looked at time "from the side", you'd see yourself as a long pink worm, starting at the moment you were conceived, and ending as you die. A slice through the worm is you at a single moment in time. So why does it matter that the worm has ends?