What might immortality mean? Say medicine eliminated death by age or disease, and distributed backups eliminated death by accident or murder. (We record your state periodically and reconstitute a new you out of raw atoms if necessary; we beam copies of your backup tapes to repositories all over the solar system, just to be paranoid.) This is the strongest sort of physical immortality I can imagine. But life is change, and how long can you keep changing before you're no longer you? Over enough time even the deepest invariants of personality will need reworking, and those old memories/recordings won't ever be invoked again, even though they're not irretrievably lost the way they are with today's version of death. And actually what we have today may not be different in essence from this scenario -- which assumes your mind's pattern is what counts, not your body. It's not just sentimental twaddle to say people live on (to some small extent) in the memories of those who knew them best; it's a natural consequence of identity-as-pattern.
But be contented when that fell arrest
Without all bail shall carry me away,
My life hath in this line some interest,
Which for memorial still with thee shall stay.
When thou reviewest this, thou dost review
The very part was consecrate to thee.
The earth can have but earth, which is his due;
My spirit is thine, the better part of me:
So then thou hast but lost the dregs of life,
The prey of worms, my body being dead;
The coward conquest of a wretch's knife,
Too base of thee to be remembered.
The worth of that, is that which it contains,
And that is this, and this with thee remains.
I think we're headed for a postbiological world where these questions will be real and everyday. I also have a feeling death and life are bigger than biology -- they were operating in some less-developed form before the first cells -- some principle about self-organizing to the edge of chaos, maybe -- and they'll still be there after the last DNA-based organism gets decommissioned. I'm all for making death less sudden, though.
If we can't banish death, then, can we put it to use? Hans Moravec has considered this question. Suppose the many-worlds interpretation of quantum mechanics is right, and there's a parallel universe for every choice that might have gone differently. Most of us want to live in a universe where we're happy and fulfilled. The most obvious way to arrange that is by simply killing yourself whenever you're not, letting your better-off selves continue on. This has an obvious problem: the psychic stress of suicide is nontrivial, even if short-lived. We might fix this bug with an autodestruct device that monitors your brain state, looking for tiny signs of discontent before you notice them yourself; whereupon it blows you up in milliseconds, too quick to experience. This looks like a real improvement, but what if it got into widespread use? Of all the people popping off left and right, maybe your own Autodestructorizer will allow you to experience only the deaths you don't care about, but that seems like a lot to ask. So here's our Mark II model: when it notices anything going wrong, it instantly destroys our entire universe. (Instantly means a wave of destruction traveling out at lightspeed, maybe caused by a phase change in the vacuum.) Now we're getting somewhere: only universes where everyone's happy survive. (If this sounds profligate, remember we're assuming an unlimited number.)
That wasn't quite right: we get universes where everyone's happy, but also ones where someone's machinery broke. Even with fail-safes, it takes heroic engineering indeed to make the first outcome more likely than the second. (In this design context, fail safe means failing by blowing up.) One might also object that by continuous local optimization of people's mental states, we're precluding global improvements -- what you might call the watched-pot effect. And there's something robotic about the kind of people we'd get, however human they are in our context. I think it's too soon to give up on trans-universal engineering, but certainly all this is discouraging.
We've considered deliberate biasing of survival rates over one's population of selves, but the natural rates can lead into strange territory, too. Only those of you who are alive have experiences; as you get older your life gets less and less likely. By the time you're 150 the universes still supporting your consciousness manage it only by aliens from outer space keeping your brain in a vat, or something. Fortunately (at least if you don't enjoy that sort of unending bizarre inhuman torture), natural deaths usually aren't instantaneous, so your future's more likely to include an experience of death. Unfortunately, death is not absolutely irreversible; it's but how we define a cessation of experience we don't yet know how to cure. For each of your likely natural ends, there will be an unlikely extension: perhaps the aliens land and rush medical nanobots to your aid. Since only the worlds where you exist are relevant to your personal future, it seems you must expect a bizarre and unnatural afterlife. Death will not release you.
Death is the liberator of him whom freedom cannot release, the physician of him whom medicine cannot cure, and the comforter of him whom time cannot console.
-- Charles Caleb Colton