Humanity's quest for these have been motifs of fiction for probably as long as there has been fiction; mythical adventurers seeking the elixir of life, that sort of thing.
Recently science fiction has offered a whole new way of living forever - in fact, several:
- Vampire legends have allowed a form of eternal life for many years; although this largely belongs in the fantasy/horror genres, there is no reason not to invent a science fiction twist to the original legend (which, in itself, can be seen as a subversion of the Christian communion, but that's another subject).
- In Red Dwarf, Lister extended his life by 3 million years by going into stasis, thus comfortably outliving the entire human race. Despite still being 'mortal', Lister's predicament nicely illustrates one of the less desirable potential side-effects of immortalilty.
- Advances in medical science can be extrapolated or invented to cure almost anything, slow down aging, and extend life for as long as is necessary for the story in hand.
- Probably the most spiritual form of eternal life in contemporary sf is 'ascension'; in Stargate: SG-1, Daniel Jackson ascends to become a being of pure energy, exisiting on a higher state of existence. However, in Jackson's case at least, the process transpired to be reversable.
- Eternal life in cyberspace. I guess this kind of idea was a part of the Cyberpunk genre: the uploading of one's memories and personality into a huge computer system where it can live on long after the expiration date of the physical form.
- Taking the concept a step further, in The Sixth Day, personality and memories can be uploaded into a clone of the physical form repeatedly, effectively extending life indefinitely.
- Douglas Adams, in typical Douglas Adams style, created an immortal character - Wowbagger the Infinitely Prolonged - who 'had had his imortality inadvertantly thrust upon him by an unfortunate accident with an irrational particle accelerator, a liquid lunch and a pair of rubber bands.'
And since I can't possibly hope to top that sentence, I shall offer today's poser (borrowed from a cyberpunk story, I think Greg Egan's Permutation City):
If a simulation is perfect in every way, is it still a simulation, or is it the real thing?
For instance, is a clone of you, with your personality and memories, you? If both exist at once, which is the real you? And how do you know?
Perhaps more relavent to the Christian worldview, does the clone have a soul? Does the cyberspace copy of you?
Another interesting point from the Christian worldview is that if you could physically live forever, you wouldn't need Christ's salvation to gain eternal life. Or to put it another way, rather than 'dying to sin', you would have to physically die in order to receive it.