I've long been enamored of the Many-Worlds Hypothesis. This is one of the explanations for some aspects of quantum physics: in a nutshell, it essentially says that everything that can possibly happen does in some sense happen -- that the world is constantly forking, a zillion times a second, into a plethora of alternate realities. It's "Worlds of If" on steroids. A lot of physicists hate it because it involves numbers that become insanely large (even by cosmological standards) very quickly, but I don't find that a compelling counter-argument by itself. And it does help explain a lot of philosophical conundrums, even while it forces one to reconsider the meaning of a lot of comforting concepts like Identity.
I'm equally fond of The Anthropic Principle. This is a way of wending one's way through Many-Worlds, and addresses the problem that our universe seems to have a bunch of rules and constants that are at once irritatingly arbitrary-seeming, and yet seem necessary in order to support life. Some people would take that fact as evidence of Intelligent Design, but the Anthropic Principle simply observes that, if the universe *couldn't* support life, we couldn't make the observations. So if there *are* a near-infinite number of realities out there, of course we will happen to evolve in the ones where we are able to exist, no matter how finely-balanced those realities have to be.
I am amused, though, that no one seems to follow these arguments through to their ridiculous but logical extreme. If everything is possible, and I (as an individual) can only make my observations in a reality where I exist, then I am, in a strange sense, immortal. Oh, virtually every reality winds up with me ending in my alloted six score and ten, but I'm never going to wake up one day and say, "Hey, look -- I'm dead." The other realities -- the ever-less-likely ones where I just keep somehow surviving -- will always be the ones where I am around to make my observations.
Mind, that isn't a wholly good thing: "alive" isn't the same thing as "happy". Carry this logic all the way through, and you get that narrow slice of probability where I wind up, the last brain in a jar, screaming its lonely way through time until dark energy finally rends its atoms asunder in the heat death of the universe. There's a creepy science fiction vignette for you.
And as previously mentioned, the Many-Worlds Hypothesis forces one into a much more nuanced definition of Identity: saying that I am immortal doesn't quite mean the same thing when "I" am not a very well-defined concept. But that's a posting for another day (or night)...