In "The Cask of Amontillado," to whom is Montresor telling this story?
There is some evidence to suggest that Montresor might be speaking to a priest. In the beginning, he addresses someone who, he says, "well know[s] the nature of [his] soul." A priest, certainly, would be one to whom Montresor might have made confession in the past, and, in this way, such an auditor would absolutely understand Montresor and know him quite well.
Secondly, Montresor does seem to be confessing now. In the end, he says that the events of this story took place "half of a century" ago. This means that he is now an old man. If he was in his mid-twenties when these events took place, he'd be in his mid-seventies now. It is possible, then, that he is making his final confession to a priest before receiving his last rites. If he has held onto this information for so many years, it might have been weighing heavily on his conscience, though he only now confesses (when he's so near death) because he doesn't want to suffer any consequences for his actions. After all, he said in the first paragraph of the story that, in order to exact revenge, "[he] must not only punish, but punish with impunity." This means that he felt he had to punish Fortunato and also avoid punishment himself. Now, however, as an old man possibly about to die, he may want to get it off his conscience.
Finally, the Latin phrase at the end, "In pace requiescat!" (translation: rest in peace) makes it seem all the more likely that Montresor is Catholic and that he could be speaking to a priest. It is unclear whether Montresor is speaking of Fortunato or of himself when he says this. Maybe he speaks of both! If he is speaking of himself, then perhaps he hopes he can rest in peace because it is possible that he has not rested peacefully these fifty years with the weight of this murder on his conscience. If he is speaking of Fortunato, maybe he now regrets what he did, or at least recognizes that he didn't get away with the murder without consequence. His guilt may have followed him all this time.
Poe is the original master of suspense, and this short story, "The Cask of Amontillado," is evidence of that fact. The narrator talks to an invisible and unknowable audience (us), but there is someone else to whom he speaks. He says:
The thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult I vowed revenge. You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat. At length I would be avenged....
These few lines establish one clear fact: the specific person to whom Montressor addresses these lines is someone who knows him well. We simply get to listen in on the story. The fact that he's telling this story fifty years after the fact suggests this is perhaps a letter or some other kind of written work, which means it could have been just about anyone who was at least somewhat familiar with the two main characters and this setting.
To answer your question, then, we can't be sure whom, exactly, Montressor is addressing. We know it was someone who knew him well and would, therefore, presumably not be as shocked as we are to hear about this outrageous episode in Montressor's life.
Readers are never told exactly who Montresor is telling this story to. We do know that he is telling this story many years after having killed Fortunato. The story ends with the narrator saying that it has been half of a century since the two men went down into that cellar.
I do not think that Montresor is specifically telling readers about that night though. I originally thought that Montresor is "speaking" to us (the reader) because he says "you." It's like he is directly addressing me or any other reader; however, I no longer think that is true. The full line that I am thinking of is the following line.
You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat.
Montresor can't be talking to me or some other nameless reader. He has to be talking to somebody that knows him. I don't know Montresor at all, so I can't know the nature of his soul. He must be talking to somebody that knows him well enough to know that Montresor is not somebody that announces his intentions to people. Readers essentially get to eavesdrop on this conversation between Montresor and the other person.