Death is the gift of men in Tolkien's Lord of the Rings, and a little appreciated one it usually is. Several articles and news stories in the October 8 issue of Nature argue that we have reached the limit - and that nobody is likely to get much older than 120. The editorial linked above argues that major life extension is probably not feasible and that we shouldn't even try.
Could it be possible, in some science-fictional future, to break free from the bonds of human life expectancy and increase lifespan indefinitely? An unquenchable desire for eternal life has preoccupied humanity from the earliest times, as attested by the earliest passages of the Bible, the Gilgamesh epic and many other stories from our past. Perhaps the chilliest evocation of mortality comes in Bede’s seventh-century Ecclesiastical History of the English People, in which a chieftain remarks that the ‘few moments of comfort’ offered by human life are as the brief flight of a sparrow through a warm and lighted mead hall, in through one door, and out through the other, back into a dark, storm-tossed and demon-haunted night of which we know nothing. No wonder we’d all like a little more light. Technological solutions might one day transcend the limitations of the human body, but transcend them they must — mere extension is already yielding diminishing returns.
The risks of transcendence are twofold. First, it might be that to extend our lives beyond our normal span, we must somehow become other than human. After all, what would a 50-year-old hamster be like? The unintended consequences of immortality are graphically and grimly illustrated in Aldous Huxley’s 1939 novel After Many A Summer, in which people fed on a life-extending diet of carp intestines live for centuries — at the cost of turning into witless apes. Second, there is a risk that life wouldn’t really be that much longer — it would only feel like it.
Appeal to one old SF story seems weird to me, but there are some more obvious problems, also explored in SF forever. If some can live almost forever, clearly most cannot, unless reproduction is shut down completely.