In Superman III when he enters the cave, the 1st thing the villain does is shoot a forcefield around Superman and says, "Let's see how long he can survive (or go), without air." Superman doesn't require air or oxygen. He can fly/function in the vacuum of outer space, under the ground and in the ocean.
Actually he does need to breathe in order to survive, it's just that he can hold his breath for a really long time. Rewrite of the Superman mythology about the mid 80's to "reign in the character" and allow for more easily written stories according to Wikipedia.com
It's actually stated in the comics before the recent "reboot" (Batman stated this) that Superman doesn't breathe. He does it as Clark to keep up appearances.
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