What does the human body use oxygen for besides the final electron acceptor in the electron transport chain?
Superoxide, O2− is created by the immune system in phagocytes (including neutrophils, monocytes, macrophages, dendritic cells, and mast cells) which use NADPH oxidase to produce it from O2 for use against invading microorganisms. However, under normal conditions, the mitochondrial electron transport chain is a major source of O2−, converting up to perhaps 5% of O2 to superoxide. [1]
As a side note, there are two sides to this coin.  While this is a useful tool against microorganisms, the formation of the reactive oxygen species has been incriminated in autoimmune reactions and diabetes (type 1). [2]

[1] Packer L, Ed. Methods in Enzymology, Volume 349. San Diego, Calif: Academic Press; 2002
[2] Thayer TC, Delano M, et al. (2011) Superoxide production by macrophages and T cells is critical for the induction of autoreactivity and type 1 diabetes,60(8), 2144-51.