What type of music did Edgar Allen Poe like listening to?
First, it would be helpful if you clarified this. Are you looking for a factual response or an interprative response. I presume that you are looking for what kind of music Poe listened based on the type of literature he wrote. If the latter is the case, than continue reading.
Music interests can often give us insight into others' personalities. That said, it is logical to believe that Poe listened to music that reflected the themes in his literature. According to enotes, "After Poe’s death in 1849, some critics faulted [Poe's] obsession with dark and depraved themes...and is [currently] regarded [by many] as an important writer of psychological thrillers and horror." Accordingly, he likely listened to music that conveyed, either directly or indirectly, similar themes. To brainstorm, try thinking of people whose personlatiy reflects their music interests.
From a general standpoint, classical music has been shown to support higher-functioning brain activity. Thus any writer who shows those signs may enjoy listening to classic music while writing.