People bring up Wrath of Khan for being the best one but it's probably because of the pacing. I prefer Star Trek V because of the characters (that scene with McCoy and his father, damn).
I've always felt Wrath was the best movie because of both the acting, lets be honest the only person able to out ham Shatner was Montalban and even though the never actually shared a screen they feed other of each other amazingly well and the tension is palpable between the two (and of course we got the KHAAAAAAAAAAAAAN meme which is gold).
And then you have the death of Spock, which was a unforeseen gut punch. We thought that somehow Spock would be OK but his funeral scene still hits hard to this very day. Hell when I first saw Wrath I watched Spock do the thing and I was all like...pffft no way Spock dies and then BLAM! right in the feels with Kirk's farewell eulogy.
I actually don't mind III. I liked most of it in fact and it feels like a very Trek sort of film with lots of good idea's and callbacks. Plus you know Kelly doing his best Nimoy impression is down right awesome. Why it gets hated on it always a bit beyond my understanding.
Really the JJ Abrams movies were 100% missing the point of Star Trek, trying to sell it as a slick action movie for the masses rather then what Trek should be. But Nu-Hollywood missing the point of older franchises is so blatant now it's not even remotely funny.
I also think that is why Trek really is dying. The culture and attitudes of the new generations of people are just not compatible with the values Trek pushes..well real Trek not the Nu-Trek, so there is no real interest in it.
Maybe in another decade or so humanity will have swung back towards a more hopeful optimistic outlook on life that gels with the future Trek portrays and not this bleak nihilism that has grasped onto everyone. A time when we will look forward with hope and not backward with longing only then can Trek really come back and start over.
But hey, we had to wait over a decade for TMP and now we have many great moves and tv series to sustain us until the day someone somewhere is able to resurrect that magic that was Star Trek.