Cancer researcher, Doctor John Wynn gave an interesting talk this year. In it he argues, in short, that it is the fact of our mortality that gives our lives meaning. Which philosophers have discussed this notion, and what conclusions have they come to?
The notion that death gives meaning to life is less a well-defined theoretical position than a commonplace; it strikes me in this sense as similar to the notion that "hate and love are the closest emotions" at least insofar as it might be difficult to isolate specifically philosophical expressions of this notion, but nevertheless it is a very frequently-expressed opinion.
Now, plenty of thinkers have discussed death: Montaigne famously quipped that "to study philosophy is to learn how to die"; Seneca wrote "the whole of life is nothing but a journey to death." Other philosophers like Nietzsche might suggest that it is certainly not death which gives life a meaning; rather life only has meaning if one has goals which inspire one to live. Some existentialists like Camus (and to some extent Kierkegaard) emphasize the absurdity of life -- i.e., that not even its end could imbue it with meaning. Other sorts of thinkers indicate that love, beauty or reason are necessary to provide existence with meaning.
My sense then is that most philosophy will not simply assert that death is sufficient to endow existence with some meaning; rather we must (learn how to) provide meaning for our own lives.
You might be interested in a recent article in the New York Times, "Philosophy as an Art of Dying", which explores the theme in the context of the history of philosophy. From there:
It happens rarely, but when it does it causes a commotion of great proportions; it attracts the attention of all, becomes a popular topic for discussion and debate in marketplaces and taverns. It drives people to take sides, quarrel and fight, which for things philosophical is quite remarkable. It happened to Socrates, Hypatia, Thomas More, Giordano Bruno, Jan Patočka, and a few others. Due to an irrevocable death sentence, imminent mob execution or torture to death, these philosophers found themselves in the most paradoxical of situations: lovers of logic and rational argumentation, silenced by brute force; professional makers of discourses, banned from using the word; masters of debate and contradiction, able to argue no more. What was left of these philosophers then? Just their silence, their sheer physical presence. The only means of expression left to them, their own bodies — and dying bodies at that.
Ayn Rand wholly agrees that our mortality (that is, the ability to die) is what makes life worth living.
"It is only the concept of ‘Life’ that makes the concept of ‘Value’ possible. It is only to a living entity that things can be good or evil. … To make this point fully clear, try to imagine an immortal, indestructible robot, an entity which moves and acts, but which cannot be affected by anything, which cannot be changed in any respect, which cannot be damaged, injured, or destroyed. Such an entity would not be able to have any values; it would have nothing to gain or to lose; It could not regard anything as for or against it, as serving or threatening its welfare, as fulfilling or frustrating its interests. It could have no interests and no goals; Only a living entity can have goals or can originate them. And it is only a living organism that has the capacity for self-generated, goal-directed action." - Ayn Rand.
Mortality is a central element in Heidegger's idea of authentic living as described in Being and Time. Inauthentic living occurs from the eyes of the 'they', that is, living through the priorities and concerns of a collective entity and not one's own. Dasein (the human being questioning her own existence) more authentically engages her own possibilities through a consideration of her own mortality. An example is the commonplace story of a man realizing that he has wasted his life after a near-death experience or witnessing the death of another.