For some, toning down the Fan Service by several notches to focus on the more important fighting mechanics. For many, the inclusion of Virtua Fighter characters!
Broken Base: The fanbase is split into two main factions: Those that prefer the original fighting series, and those who prefer the soft-porn beach side-series. Similarly, the second faction is in itself split over whether or not to include an official nude option (which, aside from various hacks within those games and an April Fools Day joke from EGM, no such option actually exists).
And now there's a new split based on the announcement by Team Ninja that they're toning down the fanservice (and breast sizes) in Dead Or Alive 5.
Well, at least the breast sizes don't look too affected…
The less obvious but arguably more important split is between competitive players who want the counter system from 4 toned down and those who prefer the system from 4 because it prevents people from using Combos.
Complete Monster: Donovan: He's the one who arranged for Christie to murder Helena's parents death, and is pretty much responsible for everything wrong in the series, and if Dimensions's stinger is anything to go by, he's also using the mask he created to become stronger.
Also, in Dead or Alive 2's story mode: in both the cutscene before Lei Fang's battle with Helena and Lei Fang's winquote after, the game gives the impression that Lei Fang is flirting with her opponent.
The movie. Dear lord the movie. After the Kasumi\Leon fight trashes her room Christie is thankful for Tina letting her sleep with her. When Bass comes around, Christie can't help but play it up to Tina's horror.
Christie's attitude towards Helena crosses into this at times.
Older Than They Think: Some internet posters think Jann Lee's yellow tracksuit is a Shout-Out to Kill Bill, but it was actually first worn by Bruce Lee in Game of Death which Kill Bill was referencing. Which makes sense, since Jann Lee is a Bruce Lee Clone.
Base Breaker: Eliot. He might be good gameplay-wise but many people just don't like him. Possibly because his 4th costume looks like something by Square Enix. At the same time, many like Eliot because he isn't muscular and has a calm, nice personality.
Similarly, La Mariposa/Lisa also gets quite a bit of hate for her personality and fighting style.
Among the games themselves, the later games (especially 4) can be considered this, especially with the counters getting progressively easier to do. A common accusation thrown by fighting game fans is that the counters killed off any sort of offense in the game since everything is easily countered.
Video Game Movies Suck: It took a full year for the DOA movie to be released in North America after being shown in Europe, and even then it quietly slipped in and out of theaters with zero promotion; given the nature of the game itself, this may be a Guilty Pleasure to some.