Readers are never given a specific answer to this question. The opening paragraph of the story explains to readers that Montresor has apparently tolerated a thousand injuries from Fortunato. Montresor draws the line at insults. When Fortunato insulted him, Montresor vowed revenge.

The thousand injuries of Fortunato I had borne as I best could; but when he ventured upon insult, I vowed revenge.

It must have been some insult for Montresor to kill Fortunato on account of it. The story doesn't tell readers what exactly the infraction was, allowing for countless possibilities. We begin thinking of all kinds of possible insults in all kinds of various situations. Then there is always the possibility that the insult was nothing more than a light tease, and Montresor is just the kind of person that can't take a joke. It's also conceivably possible that Montresor is a sociopath, psychopath, and serial killer, and he's just looking for the smallest excuse to identify his next victim. If the story had given us a clear-cut answer, then readers wouldn't get to endlessly debate about Montresor's character.

We do not actually know, with any certainty, what crimes Fortunato has committed against Montresor.  In the first line of the story, Montresor claims that Fortunato has injured him a "thousand" times, and when Fortunato, at last, "insult[ed]" him, Montresor had finally had enough.  Evidently, whatever injuries Montresor has sustained at the hands of Fortunato, they had more to do with wounding his pride than his person.  When Montresor speaks to Fortunato about confirming that a pipe of wine he recently, hastily, purchased is, indeed, Amontillado, Fortunato seems to enjoy the idea that Montresor has made a mistake.  He exclaims, "'Amontillado?  A pipe?  Impossible!'"  Despite his apparent illness, Fortunato insists that he accompany Montresor into his vaults to see this wine.  Even on the way to see this alleged wine, he insults Montresor by insisting that he could not possibly be a Freemason.  Therefore, it seems likely that Fortunato's only crimes are being a bit mean-spirited and wounding Montresor's pride.