You know I've always considered the subject of physical immortality impossible and just a bad science fiction idea.
Until I stumbled onto some articles on Turriptosis Nutricula; A jellyfish with no natural limits to its life span!
It is considered to be the world's only biologically immortal animal!
Not only that, but we've already partially sequenced their RNA: http://www.ncbi.nlm.nih.gov/nuccore/183228429
The critter can basically self regenerate itself through something called transdifferentiation - It is able to turn different types of cells into cells it needs to regenerate it's tissues.
This basically made me shut the hell up with all my negativism on the possibilities that we can ever achieve biological immortality.
If nature can and has done it, then it's only a matter of time, money and technology until we replicate the process.
Micro biology and Synthetic biology are booming sciences right now and will probably be the next paradigm shift for our generation!
So basically if immortality becomes possible in the future...
Well should we?
I don't know, but I'm starting to think it will be useful for us to start asking ourselves those questions.
Personally I think that achieving immortality will be the doom of our species, it will stall progress and innovation, which as embarrassing as it is to point out: Relies mostly on waiting the previous generation to finally die out and leave the young guys to do their thing :D
Asimov has written extensively on the possibility that a culture with un-naturally prolonged life cycle will only stagnate and wont innovate beyond creature comforts and essentials. And in the end will be replaced by other more energetic and innovative civilisations.
Short life-span means an accelerated rate of creativity and ingenuity!
Even if we do not achieve immortality what would a civilisation where people live to be in the hundreds be like?
And if you had dozens of decades ahead of you, would you ever take any risks in your life?