How do cats survive falling from great heights?
The reason why cats are superb jumpers has not received much attention, but one article in Nature was entirely devoted to just this (Diamond, 1988). Here follows a partly quoted and partly adapted text from this article:

First , because mass increases as the cube, but surface area as the square of linear dimensions, falling large animals are in general more injury-prone than small ones, as they suffer greater impact stress, their bones experience greater stress, and they reach higher terminal velocities in free-fall because of a less favorable area/mass ratio. While a small drop breaks an elephant's leg, a falling mouse reaches terminal velocity in the atmosphere much sooner and at a much lower value than do falling elephants. 

Second, falling cats have a superb vesti­bular system and make gyroscopic turns
such that all four feet are soon pointing downwards, regardless of the cat's
orientation at the start of the fall. Hence cats dissipate the impact force over all four limbs. Falling human adults  tend to tumble uncontrollably but land most often
on two feet, next most often on their heads. These facts contribute to the low mortality of falling cats and to their low chance of breaking limbs after the fall.

Third, a cat falling in the atmosphere reaches a terminal  velocity  of  about  60 m.p.h. (compared with 120 m.p.h. for adult humans) after only  about  100 feet. As long as it experiences acceleration, the cat probably extends its limbs reflexively , but on reaching terminal velocity it may relax and extend the limbs more horizontally in flying-squirrel fashion, thus not only reducing the velocity of fall but also absorbing the  impact  over  a greater  area of its body. This may explain the para­doxical decrease of mortality and injury in cats that fall more than 100 feet.

Finally, cats that land with their limbs flexed dissipate much of the impact force through soft tissue. Parachutists are trained to dissipate impact forces by landing with knees and hips flexed, then rolling.

Reference
Diamond. Nature 1988; 332:586-7  

Further reading
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