Doing A Cheetah, Jaguar or Leopard
Why Bodypaint?
Bodypaint is cool because it's unusual.
It's possible to just roll-on or sponge-on body paint, but for some effects you need a semi-pro airbrush artist to apply it to you.  Don't even think about airbrushing your own backside! You could hurt yourself!
Advantage:  you will definitely have the really unique costume at the party. 
Another Advantage:  your costume will never look the same twice.
Bodypaint is generally hypoallergenic acrylic paint, perhaps mixed with some of the same ingredients one finds in cold cream or skin creme.  An alternative is latex paint, which is more durable.  You could apply it at home and it won't rub off on your car seat.   Latex is more difficult to remove.  If you're wearing the costume outdoors in the sun you may wish to have sunscreen mixed with acrylic, applied at the venue where you'll wear the costume.  
For leopards and cheetahs, airbrush the back with shades or burnt siena to tan and the front with white.  Then apply the spots or rosettes with airbrush, spraying directly or through a stencil.  Alternatively you may wish to make a stamping device like a rubber stamp out of a fine-grade piece of foam or sponge and just stamp on the spots.
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