How bout the famous Schrodinger's Cat paradox?
The hypothesis arose from a thought experiment envisioned by Erwin Schrodinger, the founder of quantum mechanics. In Schrodinger's thought experiment, a cat is placed in a box. Inside the box is a canister of cyanide, a Geiger counter, and an amount of radioactive material so small that there is a 50/50 chance that the Geiger counter will detect radiation. If the Geiger counter detects radiation, a hammer smashes the canister and the cat dies. Otherwise, the cat lives. (If you ask me, Schrodinger was one sick puppy.) The famous Schrodinger's Cat paradox arises when an observer attempts to compute the cat's wave function: before the box is opened, the wave function is the sum of that of a live cat and that of a dead cat. In a sense, the cat is both alive and dead. The many-worlds hypothesis seeks to resolve the paradox by saying that there are two universes, one with a live cat and one with a dead cat.
This is all well and good, except for the fact that in each of these universes the observer computes the cat's wave function and still finds that the cat is both alive and dead! The paradox remains.
The paradox is resolved by noting that the wave function is a subjective quantity dependent on the amount of information the observer has. If someone peeks into the box before computing the wave function, he/she will get a wave function consistent with either a live cat or a dead cat. If someone else comes along later, not knowing what has happened, that person will get a wave function which is half live cat and half dead cat.