If you don't know the plot, I'll try to summarize it without ruining anything. Edmond Dantes is a sailor just about to marry the woman of his dreams and become captain of the ship he's been sailing on for years when he is betrayed by men jealous of his good fortunes. He is sent to a prison where he meets a fellow prisoner who tells him of a fortune hidden on the island of Monte Cristo. Eventually Edmond escapes, retrieves the fortune, and uses it to give himself a new name and identity and get revenge on the people who ruined his life.
The book, movie, and anime (Gankutsuou: The Count of Monte Cristo) all share this general story. What's really interesting is all the differences between the three versions. The book is easily the most complex of all three. There are four men on whom Edmond wants revenge and one man who Edmond needs to repay for trying to help him while he was imprisoned. Edmond uses each man's interests to get revenge (he bankrupts the banker, tarnishes the name of the politician, etc). He also uses their children against their parents, which becomes really interesting when the son of the man he tries to help falls in love with the daughter of one of the men he has declared revenge on.
The movie is understandably simplified in many ways. One of the conspirators that got Edmond sent to prison in the book is not in the movie. The methods of revenge are very simplified. There are significantly less children and wives in the movie, so less people to complicate the plot. I truly respect everyone involved in making this movie since despite so much simplification, the plot is very clear and nothing is ruined by what isn't in the movie. It remains my second favorite movie of all time.
The anime is very interesting because the main plot stays much truer to the book, but the setting is a heck of a lot more sci-fi. The Count of Monte Cristo is a space vampire, his cohorts are aliens, there are spaceships (obviously), and yet there are horses, stage coaches, and sword fights. Oh, the sword fights take place in giant robotic suits of armor.
The thing I find the most interesting about all of them is a recurring theme that is different in each one. In the book, Edmond sees himself as an avenger of God's. So everything he does is righteous in his eyes (which of course gets challenged a few times). In the movie, Edmond feels God has abandoned him and so has no problem with getting revenge by any means. In the anime, (it's hard to explain without spoiling something crucial, so bear with me) Edmond seeks revenge because he must feel strong emotions (like hate) or he will die.
I highly recommend the book or movie. The anime is interesting and worth watching, but it's a little too weird and there are some animation styles that bothered me a little too much. It does have giant robot suits of armor, though...I'd also recommend the TV show Revenge, which is the closest to a modern day equivalent that we have.