@ Justanotheratheist :
Actually, yes, each stage of a Saturn V does burn oxygen. However, it doesn't burn just oxygen, it burns the oxygen with something else. The first stage burns liquid oxygen (LO2) with kerosene. The second and third stages burn liquid oxygen with liquid hydrogen (LH2).
Why? I'm glad you asked! LO2 + Kerosene gives more thrust than LO2 + LH2, but is less efficient. At the beginning of the launch, you need raw lifting power to get you off the launch pad and up above the atmosphere. Later on, you need greater efficiency so you can build up as much lateral velocity as possible. Only if you're 200 miles up and going 17,500 miles per hour sideways will you be in Low Earth Orbit.
When you "burn" something normally (a gallon of gasoline, a Bible, etc.), you're also burning oxygen with it -- the only difference is, in a bonfire you're getting the oxygen from the air, while in a liquid-fuelled rocket motor you have to carry the oxygen along with you.