Schrodinger's Cat:
Put a cat in a box with a poison flask, that will either have two outcomes:
1. The flask breaks by a spring-loaded hammer, releasing the poison, and killing the cat.
2. The flask stays intact, keeping the cat alive.
We cannot tell from the outside of the box whether the cat is alive or dead at any moment in time. We are thus forced to conclude that the cat is both alive and dead at the same time.
Or, we can assume that the cat is necessarily alive in a different plane of existence which branches off from that point in time.
Pretty deep stuff.