The genre of "Revenge Movie" is one that I made up myself (I think?) But, basically it has to deal with the issue of revenge, so it is a classical drama, meaning that someone will die by the end of the movie.
Truthfully, in our current society, we have so many rules that bind us to not take revenge out as we would perhaps imagine, or even subconsciously desire or hope to do. I admit this, unlike so many hypocritical people in this world. There are times that something angers us and we want to take revenge, but we know that it is the wrong thing to do. However, in the film world, we can experience getting revenge (and perhaps Justice) which forms the attraction of the "Revenge Film."
In my collection, I think the following films are classic "Revenge Films:"
This movie is the best revenge film ever made!Bruce Lee is out to get revenge for his sister and for his Shaolin temple's lost honor. The whole movie is revenge and nothing but it.
2. "Pulp Fiction" (Samuel L. Jackson, Bruce Willis, John Travolta)
In some sense, almost every character gets revenge in this movie, or is a victim of another character. The movie starts out with a gangster revenge hit, and then the fight between Marcellus Wallace and Butch, followed by Butch getting revenge on Vincent Vega.
An SF movie, but pure revenge. This is for certain when Ripley says to Burke "You're going out there to destroy, not to collect?" And later she says "I say we take off and nuke the whole site from orbit." She is bent on destroying the aliens at any cost.
This one falls into the revenge category because Sarah Conner is out to get revenge on Skynet, Terminators, and the future. The crux of the movie is the phrase "...no fate but what we make..." which is the true mantra of any revenge film. And, Sarah takes this out when she goes to kill Miles Dawson and prevent him from inventing the CPU for the Terminator.
I didn't like Vol. 1 very much, and I thought it was a martial arts film without a real story. The story comes out here, and The Bride is really our for revenge against Bill, which she finally gets in the end.
There are many other movies that could make the list or get an "honorable mention" in this genre.