Story generation, or occasionally automated storytelling, is the keyword for systems that aim to write complete stories, with a narrative structure. There is also a field of natural language generation (NLG) that more broadly looks at generating text (for various purposes); it's a much bigger field.

This online encyclopedia entry has a decent short overview of some of the story-generation systems that have been built over the years: http://wikis.sub.uni-hamburg.de/lhn/index.php/Story_Generato...