The characters

There are not many characters in the story that's why it is possible to mention all of them:

The Narrator, a prisoner scheduled for execution. His loathing of a cat he once loved leads to his commission of a capital crime. 
The Narrator's Wife, a woman of agreeable disposition who likes animals and obtains many pets for her husband. 
First Black Cat (Pluto), a cat named Pluto that loves the narrator but irritates him when it follows him everywhere. 
Second Black Cat, a cat that resembles the first black cat and may be a reincarnation of the latter–or so the narrator may think. 
Policemen, officers who investigate the happenings at the home of the narrator. 
Servant, a person working in the narrator's household. 

As for the narrator, his character is revealed through his speech (1st person narrative) and actions (his behavior) throughout the story. The reader comes to the conclusion that inner world of this man is completely ruined by alcohol and no kindness has remained in his soul. The narrator consider all the events happed to him to be just a twist of fate and he sees no fault of his own. He belives that the cat is the reason of his misfortune. 

As for the cat, I would like to dwell upon two of them at a time because I consider the second one to be the reincarnation of the first one. So, I perceive these two characters as one. The black cat is even more a symbol than a character. Usually, people treat black cats as omens of something not very pleasant, but in this story the black cat is the symbol of justice - a power which punishes the one whose life is far from being virtuous. 

These characters (the narrator and the black cat) are interrelated in terms of confrontation. All in all, the cat becomes a winner while the narrator's life is almost over.