First, the Next Generation movies. They're uniformly mediocre. The stories fail to involve the audience: it's impossible to care about what happens.
Next, the J. J. Abrams reboots. 2009's Star Trek is a hoot in spite of the story's criminal violations of physics. 2013's Star Trek Into Darkness is a different story (ahem). It's loud and visually impressive, but the storytelling is a mess: too much happens for any of it to have an emotional impact on the audience. I also think the characterization of Spock is way, way off, especially in his confrontation with the villain.
That leaves the six movies starring the cast of The Original Series.
Star Trek: The Motion Picture is a stately bore. The best that can be said is that the crew is good at their jobs. (That's a greater compliment than you might think: keep reading.)
Star Trek II: The Wrath of Khan is most people's pick for the best of the bunch, and looking at it dispassionately I have to agree. My only criticisms are the inconsistencies between the movie and its precursor TV episode, "Space Seed", and Kirk's unaccountable failure to follow (sensible) procedure before the Enterprise's first encounter with Khan and company. This is the first obvious instance of what I call "competence rot", but it won't be the last.
Star Trek III: The Search for Spock is necessary from a continuity standpoint, but as a standalone movie it just lies there, not terrible, but not particularly great, either. On the plus side, the competence rot afflicts not Our Heroic Crew, but their would-be pursuer, the captain of U.S.S. Excelsior. Indeed, Sulu and Uhura will never fare better than this movie: they are badasses.
Star Trek IV: The Voyage Home is my favorite of the bunch, but I have to admit it's pretty silly. Its saving grace is acknowledging the silliness and maintaining an appropriately light tone throughout. Unfortunately, in keeping with that light tone, competence rot is widespread: Chekov is implausibly idiotic throughout, reaching a nadir of idiocy during his interrogation by government agents; Scotty heedlessly passes along future technology; Spock repeatedly sticks out like a sore thumb even though he is a careful and cautious observer by nature and should easily have been able to keep a lower profile.
On its release, Star Trek V: The Final Frontier displaced The Motion Picture as the worst of the original cast's movies, hands down. Competence rot is at parodic levels: Scotty bangs his head on a bulkhead immediately after boasting of his categorical knowledge of the ship's layout; Sulu and Chekov get lost on Earth; Uhura loses her head (not to mention her good taste) and falls for Scotty, of all people. The topper? The entire crew misses the approach of a hostile ship. This is a flaming wreck of a movie that, in spite of stiff competition from a couple of the Next Generation films, remains the leading contender for the worst Star Trek movie ever.
I suspect Star Trek VI: The Undiscovered Country was made because nobody wanted Star Trek V to be the original cast's final appearance: it would have been just too embarrassing for all concerned. Except for being their last hurrah, however, The Undiscovered Country isn't a particularly distinguished entry in the series: it's workmanlike but clunky. Competence rot is as embarrassing and widespread as in Star Trek V, maybe even more so. Chekov is a moron who doesn't know what happens if you fire a phaser onboard the Enterprise and can't carry out an investigation; Uhura doesn't have the vaguest grasp of the Klingon language, in spite of the Klingons being the Federation's main enemy for decades; McCoy doesn't know Sulu has his own command even though Sulu has been a captain for at least three years at the time the movie opens. Spock even (deservedly) suspects himself of losing his grip when brooding in his quarters. You know competence rot is bad when the characters comment on it.
Man ... I didn't realize the Trek movies were such a sorry lot until I wrote all this down. It's a testament to the blind loyalty of people like me that even the low quality of most of these films hasn't stopped them from making a lot of money.