An organism that can metabolize with or without oxygen (aerobic or anaerobic). A good example is yeast. When exposed to oxygen (air), yeasts follow the normal respiration reaction:
C6H12O6 + 6O2 ------> 6CO2 + 6H2O
However, when no oxygen is available, the yeast will revert to fermentation, which produces ethanol. This is the reaction used to create alcoholic beverages.
C6H12O6 -------> 2CH3CH2OH + 2CO2
Animal muscle cells also are somewhat facultative anaerobic. Normally, muscle cells utilize normal, aerobic respiration. When the muscles are working so hard that not enough oxygen can be supplied to them (e.g. sprinting, weight lifting, etc.) the cells will use anaerobic respiration. However, it is slightly different from yeast because lactic acid is produced in place of ethanol and carbon dioxide. This lactic acid is what causes muscles to "burn". (I will dispense with using chemical formulae, to save having to interpret a long lactic acid formula)
Glucose -----> Lactic Acid
It should be noted that aerobic respiration produces 18 times more energy per unit glucose than anaerobic, so the faculative organism will always choose aerobic if given a chance.