When falling, a cat is able to twist and turn so as to land on its feet. The cat uses the so-called "righting reflex", moving its legs to change its angular velocity and hence its moment of inertia. This reflex appears after a cat is several weeks old.
A falling cat's terminal velocity is 100 km/h; the falling reflex reduce injuries, but a fall can still break bones or result in death.
This reflex is not just a curiosity; the problem solved is related to applications of gauge theories in mechanics and control. For more information, see the falling cat problem.