"In the Schrödinger's cat experiment, what would happen from the cat's point of view? Would the cat's consciousness be split in two, with one consciousness living and the other vanishing into the sweet hereafter? Or would the cat, having the special status of being an observer, perceive itself as following the more fortunate fork in the quantum road and thus avoid death? To quote the Wikipedia page:

'...The idea comes from a variant of the quantum suicide thought experiment. Suppose a physicist standing beside a nuclear bomb tries to detonate it. In almost all parallel universes, the nuclear explosion will vaporize the physicist. However, there is a small set of alternate universes in which the physicist somehow survives. The idea behind quantum immortality is that the physicist is only alive in, and thus able to experience, one of the universes in which a miraculous survival occurs, even though these universes form a small subset of the possible universes. In this way, the physicist would appear, from a personal point of view, to be living forever...'

We should all hope to Ghawd that quantum immortality is a mere figment of the physicists' imaginations.

This wouldn't be immortality for one and for all. Only one person in the universe would benefit -- namely, you! Your consciousness would never cease, but all those around you (whose consciousness you don't have the privilege of sharing) would be subject to the normal limits of biology. But from their point of view, they would each be immortal, and all those around them, including you, wouldn't.

It would be a perverse form of immortality. You would live to see your family and friends grow old and die. You would live to see civilization rise, and fall. You would live to see the end of the human race. You would live until the Sun went supernova and the Earth was vaporised into a cloud of ash. And still you'd live." - link

Wikipedia Entries:
Multiverse - The idea of multiple universes explored from several angles.
Anthropic Principle - Is this just another theological truism? The debate is hot.
M-theory - One of the many versions of String Theory, the basics of which are easy to grasp and quite breath-taking.

Books:
The Universe Next Door - Marcus Chown explores the baffling universe exposed through Quantum Theory. Multiple universes, time travel, quantum weirdness and more are explored (I first read about quantum immortality in this book).
Hyperspace - Michio Kaku weaves a rich tapestry of physical theories in this book, higher dimensions of space and multiple universes being top of his list. The infinitely complex simplified.