Nothing to Be Frightened Of
Julian Barnes' "Nothing to Be Frightened Of" has a wonderful opening line, "I don't believe in God, but I miss Him." For a book examining mortality from a once atheist now agnostic author the duality captured in that line exemplifies the tone the book takes in its examination of death. I've not read anything else by Julian Barnes but picked up the book based in part on its opening line and a favorable review I read of it. Since then I see that the book graced The New York Times "10 Best Books of 2008" list.
While I have thankfully not suffered the dreaded jolt awake in the middle of the night realizing my own mortality the author vividly describes in the book, I must admit to the occasional panic attack concerning someone else's mortality (another theme touched upon in the book). The author writes not only about death but also family, memory, and legacy. The author approaches the morbid subject with the right amount of wit and decency that I highly recommend reading it.
Some of my favorite pieces from the book:
"The Pascalian bet sounds simple enough. If you believe, and God turns out not to exist, you lose, but not half as badly as you would if you chose not to believe, only to find out after death that God does exist." 
[Quoting Shostakovish] "We should think more about it [...] and accustom ourselves to the thought of death." 
[Paraphrasing Montaigne] "You should have the taste of death in your mouth and its name on your tongue. To anticipate death in this way is to release yourself from its servitude: further, if you teach someone how to die, then you teach them how to live." 
"[...] philosophizing, is practicing for death -- in the sense that he is spending time with his mind and ignoring the body which death will obliterate." 
"Do you want a distillery or a river? Life rendered as a few drops of the hard stuff, or as a litre of Normandy cider?" 
"The fury of the resurrected atheist: that would be something worth seeing." 
[Quoting Voltaire] "If God did not exist, it would be necessary to invent him." 
"[...] the additional tragedy of life is that we do not perish at the right time." 
"The better you know someone, the less well you often see them [...]" 
[Quoting Renard] "Imagine life without death. Everyday you'd want to kill yourself from despair."