Poe had an effect on two major literary genres: the short story and the detective/mystery story. From this, his influence rippled out to have an effect on prose literature as a whole.
In 1846, Poe wrote an influential essay called "The Philosophy of Composition." In it, he made two important points. He thought writers should plan their work to highlight the emotional effect they hoped to elicit from readers. For example, if the goal was to generate the emotion of fear, then all the elements of the story from setting to character to plot should be scary. Related to this is the idea of brevity. Poe thought literature should get to the point and not ramble on and on. Both of these elements supported his central idea that a work of writing should be carefully planned with the ending in mind, not simply a rambling response to inspiration.
1846 is a significant date, a time when prose fiction was still evolving and many bloated works (to our modern minds) were being written. Poe helped set the direction for the more streamlined plots and prose that are characteristic of the modern age.
Just as significantly, Poe is credited for establishing the format of the modern detective or mystery story in which a highly talented amateur uses logic and insight to solve a crime that defies the police. Poe's detective Dupin became the prototype for the modern detective from Sherlock Holmes to Hercule Poirot.