"Letting Go" by Atul Gawande is a certified Instant Classic essay.
This one isn't a masterpiece in terms of the writing, though Gwande is a good writer, nor does it really resolve the question it deals with. He just weaves a few interesting facts together with a number of very engaging stories. And that's enough.
A few thoughts: In one of his books, either Cosmopolitanism or The End of Ethics, Kwame Appiah mentions that he doesn't like the idea of rules in ethics. He doesn't think there is an algorithm for figuring out what the right thing to do is. Instead we should just try to understand stories, context, and feelings. We should read novels for ethical enlightenment.
This essay demonstrates the strengths of that kind of thinking. I do think we need to think about rules of thumb for when to stop treatment and we need to look more carefully at why hospice patients live so long--something that doesn't surprise me given what I know from positive psychology). But stories are a start.