Complete and utter immortality, in a "god-like" manner of speaking, I don't think will ever happen.
Agelessness, yes.
Extremely enhanced lifespan, yes.
The ability to be destroyed, yet have your mind/brain "saved" in a sense, and put into an exact copy of your body? Some day.
I don't think we'll ever be to the point where the entire universe would explode, and Mr. Immortal would be sitting there, writhing in pain, horrifically deformed, but still alive and kicking. Immortality is only attainable in the sense that it is assisted in some form or another. A regenerating body, a "copy" of your brain/mind/memories/knowledge, agelessness, etc.
There are ways to greatly extend your lifespan now, people just generally don't do it. I think most people born today will easily live past 100 years old. And that'll only continue as time goes on.
I wouldn't mind being immortal in the sense that I described above. Of course, godlike status wouldn't hurt :3 but a strange enough entity with power/technology far exceeding the average man's could easily be thought of by the average man as "godly". Authur C. Clarke said "Any sufficiently advanced technology is indistinguishable from magic." Who's to say that God doesn't actually exist, but his power is simply a super-advanced technology that appears to most as "mystical". That's another debate though.
But yeah, I'd take immortality. Only if I could take others with me. Reminds me of Tuck Everlasting, or at least the small bit I remember of it. While I'd love to have the freedom to explore a plethora of things in an unlimited lifespan, it wouldn't mean much if I didn't have someone (or more than one) to experience it with.
I should note that in a sense, I am afraid of death. Or maybe afraid isn't the right word, but not looking forward to it. Of course, I believe that if I die, I wont know any better. But at the same time, if I had the ability to feel anything beyond death, I'd probably be irritated. Especially if I died soon. I'd love to see events ages into the future that no other human could dream of seeing. Experience things that no one else will experience. I understand not everyone is like this, and that's fine.