Recounts. Recounts focus on retelling events and are generally intended to inform and/or entertain.
Poetry. It can be written to serve a wide variety of purposes. For example, poetry can be written to entertain, to inform, to amuse, to share knowledge, pass on culture, to advance culture etc.
Narrative. The purpose of narrative texts is to tell a story.
Persuasion Texts. Their purpose is to convince the reader of the merits of adopting a particular viewpoint or taking a specific course of action.
Expository. This text is intended to identify and characterise experiences, facts, situations, and actions in either abstract or real elements.
Drama. As with narrative texts, the purpose of drama is largely to entertain through storytelling.