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.
Evil Is Sexy: Benedetto is repeatedly described as handsome and (while in his aristocratic guise) charming.
Marty Stu: Arguably protected by Grandfather Clause, but think about it; the Count himself spends several years in prison, and in the meantime, obtains permanent night vision and manages to become a master of every common-for-the-day fighting style and several languages. Though to be fair, the latter two (mastery of multiple fighting styles and his fluency in languages) aren't impossible and in fact an educated man of the 19th century as Dantes became as the Count would be expected to speak multiple languages. Furthermore, he knew several languages as a sailor (Spanish, Italian, and probably bits of other languages), and one can image that he may have learned a little about fighting back then, too, meaning that the only unrealistic aspect is his night-vision. Arguably, just a case of tropes aren't bad.
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.
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.
The various adaptations (radio, films, TV series, etc.) offer the following tropes:
Do Not Do This Cool Thing: Remember kids, vengeance is bad. The 2002 film will demonstrate that although it appears to be totally awesome, it's nevertheless very, very bad.
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.
Hilarious in Hindsight: The 2002 film with Jim Caviezel gives him long hair and a beard from all those years of incarceration. He later played Jesus. The movie also makes Dantes the biological father of Albert Mondego (Henry Cavill). This would mean that Jesus was the father of Superman.