Schrodinger's cat is possibly one of the most puzzling Quantum thought experiments.
Logically, it would seem impossible that the cat can be in a transition of states, both dead and alive at the same time, yet this is what Quantum Physics is asserting.
Einstein summed it up best, I think, in his response to Schrodinger:
QUOTE
You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality—if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gun powder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.
Schrodinger's cat (and the EPR paradox) are the reasons that I define myself as a Quantum Skeptic. Like Einstein, I can't reconcile any of the quantum interpretations with what I perceive reality to be.