Abiogenesis refers to the process (as yet unobserved) by which non-living matter first became arranged into living organisms. The event in which abiogenesis first occurred on Earth is more commonly referred to as the creation of life.
The predominant scientific theory regarding the nature of this process involves self-organization, simple self-replicating molecules becoming gradually more complex, and processes much like those seen in evolution.
Although it is consistent with the theory of evolution, it is not part of that theory. Despite this, lack of supporting evidence for a scientific theory of abiogenesis is often used as an argument against the (vastly better-established) scientific theory of evolution.
While most mythologies include a story explaining the origins of non-supernatural life, none have so far proposed a general theory of abiogenesis. Presumably whatever mythological beings or processes first gave rise to life on Earth could also give rise to life on other planets, but this is rarely discussed in the scripture of traditional religions -- presumably because the idea of planets as large solid bodies with atmospheres was not known of when the vast majority of scripture was first written.
Some more modern religions, such as Mormonism, do have beliefs regarding life on other planets and God's involvement in their creation. (I don't know if they have a general theory of abiogenesis other than "God created all life", however. --Woozle (talk) 10:54, 20 August 2012 (EDT))