I’m attracted to the genre, pretty much for the reasons you cite, but even though I like the cheapest, shallowest B-movie revenge stories, I can’t stomach the Charles Bronson Death Wish series (haven’t seen the remake, but I’ve got my doubts). If there are sub-types, they’d be Revenge Porn. They exult in the pain of the innocent in order to heighten the audience desire for revenge (instead of using internal conflicts in the protagonist to create tension / depth).

Zack Parker’s “Scalene” is an interesting take on the revenge storyline in that it presents the same events from the avenger’s perspective, the victim’s perspective, and the avengee’s perspective. Margo Martindale (playing the same character three different ways) has never been better.

The Korean film “Lady Vengeance” uses revenge as a theme rather than simply as a plot device.