Upon thinking about the issue a lot, I've sort of decided that I'm already immortal - in a way.
Hopes about an afterlife aside, I figure, if there isn't one, it would be logically impossible to know when you're dead. I mean, if you expect to "go into the dark" - darkness is *something.* Why wouldn't someone's brain send them "into the light" as with NDE experiences? Does it matter if they're "real" if they're your very last experience? It stands to reason that your last glimmers of consciousness/subconsciousness would "last forever" from your perspective. Yep, I've taken the Phillip J. Fry stance: "Thanks to denial, I'm immortal!" (Except it's really not so much denial as it is my natural ability to think in mind screw).
As for physical immortality... Eh. I can see humans making that into a kind of Hell. If we aren't able to kill people we don't like in wars anymore, we'll probably create some kind of eternal suffering engine, because... we're us. I don't really buy into the idea that transhumanism will make us better beings. At the very least, if people get the "brain uploads to computers" thing going on, I can see us having million-year flamewars over stupid stuff. Human-created Hell.
I've played with the idea of "humans achieving immortality" in a couple of my Legend of Zelda fanfictions, actually. In "The Great Desert" and the ongoing remake of said, "The Greater Desert," Hyrule's Golden Goddesses were once humans who achieved biological immortality through science and became... excessively bored gods. They like their immortality and are optimistic about taking care of an improving the world they created, but they are bored enough to play an eternal rock-paper-scissors game with Link, Zelda and Ganondorf's souls, which makes them kind of jerktastic. Physical immortality could do that to the best of us.