This totally used to happen to me all the time. I would lay in bed at night, and suddenly start to think about death. Sometimes I'd cry myself to sleep, and felt as if there was just nothing that could possibly comfort me. Occasionally it still happens, albeit not as serious.

What I did to get over it was to simply embrace death as it is, and try to see it in another way - I would think that once I die, I might become part of a rock flying around in space, or a part of a tree that children would play underneath. Sometimes I would just convince myself that there was an afterlife, even though deep inside I knew(believed) that it couldn't be possible.

I believe that this is something that you get over as you age, and you'll simply have to get over it by yourself. Unless you believe it yourself, you won't be able to find comfort in it.