Methanogenesis is the final step in the decay of organic matter.  During the decay process, electron acceptors (such as oxygen, ferric iron, sulfate, and nitrate) become depleted, while hydrogen (H) and carbon dioxide accumulate.  Light organics produced by fermentation also accumulate.  During advanced stages of organic decay, all electron acceptors become depleted except carbon dioxide.  Carbon dioxide is a product of most catabolic processes, so it is not depleted like other potential electron acceptors.
Only methanogenesis and fermentation can occur in the absence of electron acceptors other than carbon.  Fermentation only allows the breakdown of larger organic compounds, and produces small organic compounds.  Methanogenesis effectively removes the semi-final products of decay: hydrogen, small organics, and carbon dioxide.  Without methanogenesis, a great deal of carbon (in the form of fermentation products) would accumulate in anaerobic environments.