What do you mean by 'live forever?' Do you mean until Earth is destroyed? What if you got stabbed, are you saying you won't die? In that case, no, I wouldn't want to live forever.
However, if I could live until humanity is extinct, yes, I would, I would be wisest of the humans, I would know things no one ever knew, future scientists would come to me for advice. Heh, it'd be pretty awesome. Also, I would want to age, wonder what I'd look like when I'm 50,000 years old? Sweet thoughts! Old age kind of adds to the 'wise' personality I would have. I'd live in a 21st century house while everyone lives in space stations all over the solar system, Earth wouldn't be so overcrowded, I would be an 'Earthling Aboriginal' (I don't like using Earthling - it gives the impression that humans are weak, even though we are superior.)
Scratch out aboriginal - I'll be the link between homo-sapiens-sapiens and whatever comes after them (homo-homo-sapiens-sapiens perhaps?)
Just like the homo sapiens neanderthalensis is now considered to have been more intelligent and more powerful than us if they lasted. I would be respected as more intelligent .
My own jury is still out on whether [i}I[/i] would even want to extend my life using the methods being investigated currently. See, there are a whole raft of broader social implications that need to be considered here...all things considered I'm more amenable to first encouraging a mindset that is more accepting of death as a part of life.
Yes, I mentioned before that I wouldn't want to live forever if I were invincible, so getting stabbed/shot/face peeled off my broken glass would kill me, but I would live forever if there is no external interference.
That way I would live until I am bored with life and wish to find out the truth about death.
Although if I lived for a thousand years there would probably be around... well all scientists after for examinations so that they could prolong human life.
I wouldn't be so concerned about people around you dying. You will, after all, make new friends. There's also the chance that you won't be the only 'immortal' person out there.
I don't think boredom would be a problem either. You could spending a couple of decades trying one thing out (career wise) and when you got tired of that, you could move on to something else. There's enough different careers and activities, and so many more being made all the time, that I don't think you would ever run out.
The only thing that would concern me is what happens to your body as you age. Do you hit 80, and look and feel like an 80 year old, walking around with a cane? By the time you hit 200, are you going to be a bed-ridden husk of what you once were? that would suck. However, if you can keep the body you had when you were in your 20s, then living forever would be amazing.
In short, as long as I don't degenerate with age, I would live forever. It gives you a chance to experience all of the world, instead of just a tiny portion of it.
That's of course ignoring that the range of experience that there is to be had expands exponentially compared to the fairly 'linear' nature of our experiential range :P
There's no way anybody could ever even approach all that there was to be experienced.
I also suggest that this immortality, borne from the desire to defy death and thus constitutes a non-acceptance of our developmental natures, would also cause a certain psychological distress due to the lack of aging process, the lack of referential information that feeds into our expectations both conscious and subconscious.
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Side note: I think I mentioned some novel I was writing about the nature of life (the thread was about xenomorphic life and the definitions of life itself)...well what do you know, my main character is purportedly immortal :P