9 of 11 films so far have featured a villain, but there’s no reason they have to. I don’t think we had villains in 82% of the TV episodes.
Top 10 episodes, as ranked by GEOS.tv:
The City on the Edge of Forever: No villain.
Mirror, Mirror: In a way, the heros are surrounded by villains, but they’re just people doing what people do in this world gone mad. The story isn’t about a particular Bad Guy who must be defeated, it’s just about finding a way home from this disturbing environment.
The Trouble With Tribbles: There is a villain who poisons the grain, but that’s only revealed late in the episode. The other Klingons were jerks, not villains. The episode is not about a Bad Guy whom the heroes have to defeat.
Amok Time: No villain. T’Pring is a Class A bitch, but not a villain to be defeated.
Balance of Terror: OK, this one is straightforward hero-vs-villain. However, the villain in this case is more sympathetic than most of the movie villains.
The Doomsday Machine: I guess you could call the planetkiller a villain to be defeated, but as it’s not sentient, I think it’s a stretch to call it a villain.
Space Seed: Definitely a villain.
The Devil in the Dark: There is presumed to be a villain who must be found and destroyed, but when it’s finally found she turns out not to be such a villain after all.
Journey to Babel: Like Devil in the Dark, it’s clear that somebody is up to no good, but no villain is identified until late in the episode.
The Enterprise Incident: No real villain here, unless you count the guys who are violating treaties and deceptively seducing women in furtherance of theft of sensitive technology.
All in all, TOS did not rely heavily on the formula that has been used in 9 of the 11 films, so maybe the film series shouldn’t continue to rely so heavily on it.