Quinones, flavoproteins, cytochrome c, and electrons are important elements, essential for the respiratory chain.
Oxygen in respiration plays a role of final acceptor of electrons (and turns into H2O), but there are other final acceptors of electron transport depending on the species (nitrates for Pseudomonas, Sulphites for Clostridium ...). This allows us to classify respiration in two: aerobic respiration (with oxygen) and anaerobic respiration (without oxygen but with another electron end acceptor).