Biological immortality is actually pretty close to being doable, except once you hit around 120 years old your body would be so degraded you're pretty much dead anyway.
Once we get over that massive hurdle of ageing, then we have to deal with other issues such as overpopulation and the like. Sure, your chance of dying from un-natural causes would increase every day, but if we're already packing this planet to the brim with our 50-80 year lifespan (depending on where you come from), imagine it with an average lifespan of ~700 years.
A potential solution would be restricting it to only a cluster of people, such as only those who could afford a very steep price. Politicians, philosophers, artists, scientists and CEOs would all be able to afford it, but everyone else couldn't. While this would be the simplest option and even quite logical, it would cause a lot of power struggles down the line.
I'm not too fond of the concept of the rich being immortal and the poor all dying. It's kinda like that movie "In Time", where immortality exists, time is currency, no-one ages past 25, and the rich live practically forever, whilst the poor die young. As the protagonist Will Salas (played by Justin Timberlake, no less) said in the trailer, "no-one should be immortal, if even one person has to die", though personally i'd prefer an alternative of sorts. That alternative would be rather simple, yet also rather complex and esoteric; instead of researching life extension, search for a way to continue life after the body bites the dust. Yes, i'm talking once again about inventing the afterlife.
The way i'd go about it would be like this; first surgery would be required to gradually replace one's brain with more durable components, piece by piece until your brain is immune to the flaws of maintaining an organic system, in effect being able to generate it's own power to keep all the programs and stuff running as well as being able to repair itself.
Then the new brain, which is still you due to gradual replacement instead of simply copying the brain-data, is brought to "The Mausoleums", places where the remade brains are stored and wired up to a wireless broadcast system, in effect allowing your brain to remotely-control a "proximulacra" (a simulacra that is a proxy), a body for you to walk around in and interact with the real world. Lag issues would be present as always, so maybe certain basic actions, like navigational pathfinding and basic instinct, are performed by systems onboard the proxy.
An alternative to interacting with the real world via proxy would be having a "cyberspace" world like the Matrix, though that would require extreme refinement to make it as real as real can be. This latter option would permit a sort of "virtual retirement" from the world, and if the vast majority of humanity retired to cyberspace for eternity, then perhaps the world could grow somewhat "wild" and unspoilt again, with only the cybernetic mausoleums deep within the mountains being where humanity has effect, meaning the world wouldn't be scarred by war or pollution.
However, we'd need to clean up the world quite a bit, seeking clean and safe power supplies, before we retire from reality, since it'd be rather sloppy and inconsiderate to have coal-fired power stations belching out smoke to generate the power needed to run the world and suchlike. Then again some semblance of maintenance would definitely be required to keep the digital world alive, and maybe we could actually have the proxy-people around for minds to gather important materials when we need to fabricate spare parts to maintain the world.
All in all, retiring from the physical body to a durable mecha-brain would mean that we don't take up as much space on the planet, and could create our own virtual worlds to live in, leaving the Earth to grow naturally and heal from the damaged man has inflicted. If anything it'd make an interesting sci-fi story.
But aside from that, i'd welcome a rez if I died too early, though if there was an afterlife as an alternative, i'd probably take the afterlife if I didn't have any loose ends that needed tying up. Unless it's like some sort of pseudo-Hell where people are punished forever for accumulated transgressions; in which case i'd embrace staying alive to avoid the seemingly-unfair judgement. If it were limited sentencing and rehabilitation like what Hell actually SHOULD have been written like, as well as what the penal system should be like, then i'd be ok with it; i'm always open to the concept of something being wrong with me, which I think there definitely is, and i'd probably welcome a chance to change and become a better person.