Each living cell has a metabolism (cell metabolism), as well as multicellular organisms like plants, animals and humans have a "total" metabolism that can differ from that of the individual cells. The metabolic pathways form a two-part process - one part is called catabolism - when the body uses food for energy. The other is called anabolism - when the body uses food to build or mend cells.
The halt of metabolism in a living organism is usually defined as its death. Some organisms can reduce their metabolism to almost zero for certain periods of time. Spores of fungi can survive thousands of years in that state. But every lifeform is bound to have metabolism at some point of its life cycle, with the possible exception of viruses, which use their hosts' metabolism.
The correct definition of metabolism is almost as difficult as the definition of life. For example, according to the definition above, fire has a metabolism, too (it "eats", for example, wood, converts it to heat, and disposes ashes).