"Quantum Suicide" is a thought experiment suggested by several physicists. Basically, it is the famous Schrödinger's cat experiment, but from the point of view of the cat.

A physicist sets up an apparatus that is a activated by a radioactive decay, or a single photon going a certain way, basically some quantum mechanical event that has a 50% chance of happening. If it does happen, some method of death, like a gun or poison gas, kills the physicist.

According to the Copenhagen interpretation, the physicist has a 50% chance of dying with each run of the experiment, and eventually he or she will die, but according to the Everett many worlds interpretation of quantum mechanics, this event, like every quantum mechanical event, causes two different universes to diverge. In one of these universes the physicist will survive, and in the other he or she will die. From the point of view of the physicist, the outcome is always that he or she does not die, since that is the universe experienced.

Unfortunately, (perhaps fortunately for physicists) this experiment can't really tell us anything if it were actually performed, because to an outside observer, the result would always be that the physicist would die half the time, no matter which interpretation of quantum mechanics is correct.

The problem with this is that a sort of "quantum immortality" becomes possible. Whenever a quantum event happens that means a conscious observer is removed in one universe, they will perceive the universe where that event did not happen, hence, they can never experience a universe in which they die!

Of course, one could ask: "What's so special about death? Falling asleep is loss of consciousness too." Then the Everett many worlds interpretation would lead to "quantum insomnia." (Different quantum insomnia than staying up all night doing your quantum mechanics homework) The observer would only experience worlds in which he or she never fell asleep.

If this seems ridiculous to you, or smacks of Modern Physics Abuse Syndrome, don't worry, you're in good company. Feynman's widely accepted Shut up and calculate! interpretation puts an end to these silly questions.

All facts from Wikipedia.