Some days, I wonder if I'll get lucky and manage to go the next day without thinking about the enormity of death. Yesterday, I was wrong.
Being trapped in negative patterns of thought can be unhealthy. It's best to break those patterns. Exercise is also very helpful.
One excellent text that comes from one of the parent lineages of Shambhala is the Tibetan Book of the Dead, which is basically a preparation for the Bardo, or the "in-between" stages after life. You can read more here: https://en.wikipedia.org/wiki/Bardo_Thodol
There is a vast library of teachings from our senior teachers here: http://shambhala.org/teachings-library/ Plus a bunch of recorded talks by our very controversial founder: https://www.youtube.com/results?search_query=chogyam+trungpa
For Tibetans, the practice of meditation is simply the practice of preparing for death. You are becoming familiar with your mind so you will be able to see through the delusions that arise when your mindstream is no longer attached to a physical body.
Of course, you don't necessarily have to believe in rebirth to find value in these traditions. I have found the community aspects of Shambhala to be quite supportive, even when I had doubts, which in this tradition are expected to be plentiful, and are celebrated.
Happy to answer any questions!
If this doesn't work for you, then consider the following. We are all living beings, and sometimes some of us die, and sometimes new beings are born. But who says that those living beings aren't just one big living being? Our brains tell us so. But this view is only an artifact of the brain. If our brains were all interconnected more strongly, then I bet our brains would view us as one living being. So what you can take from this is that dying is just like losing a few brain cells. This is also something that you have been doing for years (in fact billions of years). So in this view, you never die until, of course, the universe ends.
This is an interesting theory that has its roots in solipsism: the belief the world vanishes the moment you close your eyes. The fact of the matter is that it (and solipsism) just don't seem to be true, not even to solipsists. If you truly believed you were dying at every second, you'd act in all sorts of ways against your long term survival, but here you are posting on the internet.
Even if we take the position as true, it seems entirely reasonable to perceive the end of the "chain" of "yous" to be a tragic event.
> But who says that those living beings aren't just one big living being? Our brains tell us so.
Well, our brains, as well as the general evidence we see in the world around us. If we were one giant interconnected entity, dying would probably be very different. However, there's very little reason to assume that as a given - I can't talk to my dead relatives through any of my living ones.
I think this argument is perhaps more simply stated as "you were never a large part of the human race, so your death will not matter in a large way either" which is quite true, in fact. My counterpoint would be that the death of the individual rightly remains terrifying to that individual. If I were the human race, I would correctly not concern myself with the death of a few of my brain cells (and I do not, regarding my own real brain cells), but I would regard the death of the human race (myself) as truly important.
If anyone's interested, I've written about some of these kinds of arguments I've heard before: http://vincentwoo.com/2011/04/30/arguing-for-immortality/
Let's look at it another way, the enormity of death shows us the precious value of being alive. GO out and live your life! Go do what makes you happy and feel alive. If you couldn't die, you wouldn't know you were alive, like a rock.
Many of those who have come close to death claim to feel more alive than they ever have, unless they are drugged out by pain killers and such.
Why? The fact we are aware of our death is important.