That said, the idea of using a different base for respiration doesn't really require much imagination. We use oxygen because that's the environment we evolved in; any life evolving in an atmosphere without oxygen will use something else. Even advanced life forms could use non-oxygen molecules for respiration, the only requirement being that whatever their circulatory system used could bind with, and carry, the molecule (making the very limiting assumption that their system would work similar to ours).
We have on our planet microbes that do not respirate oxygen, and are in fact killed by an oxygen atmosphere. Our advanced oxygen breathers are not even limited to a single carrying element. Sure, the land O2 users have iron based blood, but there is O2 "breathing" sea life that has copper based blood (and no, it's not green.... Roddenberry got that wrong), and others with a copper/vanadium hybrid based blood (which is green, but a bright yellow green).
Life will use what's available; no oxygen... probably not problem.