Answer
No ATP or water would be formed. Any oxidative phosphorylation would come to a halt.
Work Step by Step
The function of oxygen in the electron transport chain is as an electron acceptor. That is, when $\mathrm{H}^+$ protons cross the mitochondrial membrane through ATP synthase, they form water with the oxygen and electrons.
So, if there were no oxygen, this water would not be formed. Additionally, there would then be a buildup of $\mathrm{H}^+$ protons inside the mitochondrion, since they are no longer being transformed into water.
This buildup increases internal $\mathrm{H}^+$ concentration substantially and will cause dynamic equilibrium to be reached, meaning that $\mathrm{H}^+$ protons no longer will cross the membrane through ATP synthase, halting the production of ATP molecules as well.
