Although he's presented as/intended as an Antihero, for a large part of the book, the Count is, arguably, a Villain Protagonist. He does manipulate a greedy wife into poisoning almost every single member of her family, including one Kick the Dog moment outside the count's immediate control where she poisons her nine-year-old son. His revenge scheme even include killing his former lover's son and he made a point that his revenge aimed every child of mature age.
Villefort can actually come across as less evil/jerkassed than the other three despite his rather worse crimes (such as knowingly locking away a (actually innocent) man in the off-chance his talking might damage his career, covering up a crime committed by a relative, having an affair that results in an illegitimate child, burying said child alive) due to the fact that he does seem to be a loving-if-stern father to Valentine and Edouard, and his increasing breakdown as his household is the target of several murders (for a crown attorney, this is even worse than usual). Even the attempted infanticide is lessened when we see what kind of person Benedetto grew up to be.
Are the similarities between the half brothers Edouard and Benedetto the result of nature or nurture?
As evidence of the former are all the crimes committed by their father and the fact that both displayed the exact same Spoiled Brat tendencies as children despite being brought up in distinctly dissimilar circumstances.
As evidence of the later is the fact that neither their grandfather nor their shared half-sister ever displayed any jerkass tendencies, and that both boys were spoiled rotten by their respective mother figures.
Evil Is Sexy: Benedetto is repeatedly described as handsome and (while in his aristocratic guise) charming.
Magnificent Bastard: Once a naive boy, Edmond Dantes, the titular Count, is a ruthless schemer who will stop at nothing to take revenge. Taking his time to study his betrayers under his new identity, Dantes convinces his enemies to invest with him, knowing he will ruin them. Winning the loyalty of Albert Morcerf by saving him from a kidnapping he himself arranged, Dantes proceeds to reveal the existence of the surviving daughter of the ruler Albert's father betrayed to ruin him, as well as the bastard son of one of his other enemies after having introduced his wife to poison to destroy his household.
Misaimed Fandom: Readers are often left fascinated with the Count's overly-elaborate revenge plots, to the point that modern adaptations often just focus on the revenge and none of the moral nuances of the original novel. In fact, the author himself portrays the Count as morally questionable, and the final part of the book is spent on Dantes realizing he went too far and trying to make amends for it.
Older Than They Think: Among other things, the book is one of the first to introduce invisible ink and the treasure map as concepts, and the scheme employed to bankrupt Danglars is not only a version of the con known as "the wire", but is essentially the same trick done in the Eddie Murphy movie, Trading Places. Also, although invisible ink was used earlier by Edgar Allan Poe in his story "The Gold Bug", this novel is one of the earlier uses of the idea before it became a cliche.
"Seinfeld" Is Unfunny: With the large number of revenge stories that have cropped up to ape this one since its publication (including many a Revenge Fic), it can be hard to see why this particular story is seen as a classic.
An in-universe one: several characters note that Albert apologizing for insulting the count, having learned of his father's behavior, comes off as dishonourable; apologizing to someone you'd challenged to a duel and backing down from the duel was seen as deep cowardice. One claims that "had my father committed ten Janinas, I would only have seen fit to fight ten times".
The Count owning slaves is an In-Universe one, as several characters note, but since he claims to be of any nationality but French he gets a pass. The fact that his slaves are In Name Only (especially Haydee) also helps for modern audiences.
Values Resonance: The book is quite shockingly ahead of its time in presenting a sympathetic homosexual couple (even if Dumas couldn't ever actually come out and say it at the time) who get a happy ending. In a time when a lot more attention has been called to the problematic use of Bury Your Gays, it's quite nice that it didn't happen to one of the very first such couples in popular entertainment.
The various adaptations (radio, films, TV series, etc.) offer the following tropes:
The Man That I Used To Be is wonderfully multilayered. It starts with a subtle, dark tune as the Count retrospects on his revenge, then into a lighter, kinder tune as he remembers who he was before revenge consumed him, before ending in a triumphant climax as he reconciles the two and resolves to move forward without losing sight of either part of his past. It's a beautiful, hopeful theme that fits with the musical's more upbeat ending.
Germans Love David Hasselhoff: As seen in the comments to the above video, people from several countries all over the world watched the 1973 series as kids and remember it fondly.
Fan-Preferred Couple: Edmond/Mercedes, which is incorporated into most adaptations of the novel. This is most likely partly due to Edmond/Haydee being a case of Wife Husbandry (done by the wife, but still). One series even pairs Haydée off with Franz d'Epinay.