"Make no mistake: I should fight a duel for a trifle, an insult, a contradiction, a slap—and all the more merrily for knowing that, thanks to the skill I have acquired in all physical exercises and long experience of danger, I should be more or less certain of killing my opponent. Oh, yes, indeed, I should fight a duel for any of these things; but in return for a slow, deep, infinite, eternal pain, I should return as nearly as possible a pain equivalent to the one inflicted on me. An eye for an eye, a tooth for a tooth, as they say in the East, those men who are the elect of creation, and who have learnt to make a life of dreams and paradise a reality." (35.42)
The Count's notions regarding revenge seem to be taken solely from the Old Testament. He doesn't acknowledge Jesus' commandment to "turn the other cheek."
"Oh, God," said Monte Cristo, "your vengeance may sometimes be slow in coming, but I think that then it is all the more complete." (83.7)
As the saying goes, "Revenge is a dish best served cold." Here, Monte Cristo seems to agree with the conventional wisdom.
"Poor young man!" Monte Cristo muttered, so low that even he could not hear these words of compassion as he spoke them. "It is written that the sins of the father shall be visited on the sons, even to the third and forth generation." (85.135)
Monte Cristo, on the other hand, clearly doesn't believe that there are any extenuating circumstances. Revenge is revenge, and nothing should interfere with it, even across generations.