Even though I have issues with the Kelvin Universe, deciding to do a sort of sideways-reboot of everything could be characterized as crazy. I remember that when Vulcan was destroyed in Star Trek 09 thinking "WTF?" in the theater. And, credit to JJ Abrams, it was a moment for the audience where you knew that this was not going to be the same Star Trek universe as you knew it.
The biggest "crazy" moment for me as a kid watching Trek, where I had no idea how they were gonna resolve it, was “Best of Both Worlds” and the “Mr. Worf, fire” moment. Years later, it was interesting reading some of what was going on behind-the scenes, where at the time there was speculation that maybe the entire thing was connected to contract negotiations with Patrick Stewart, and the Borg storyline may have been an attempt to write him off the show and turn TNG into a Riker show if the negotiations fell through.
Deep Space Nine has 3 that come to mind, but they're more character-centric.
Sisko poisoning the Maquis colony in "For the Uniform" seemed like a crazy way to resolve the conflict in the episode, and I've seen people argue about it online. But when it's coupled with Sisko's actions in "In the Pale Moonlight," it points to the part of Sisko's character where he's able to bend the rules for he considers the greater good. Whether people agree with his intentions or not, the result is that writers turned the lead character into a murderer. The final lines of the episode (i.e., So I will learn to live with it. Because I can live with it. I can live with it… Computer, erase that entire personal log.") leads to an interesting argument of whether Sisko can really live with it and that's why he's erasing evidence, or if his deleting the log points to the fact that on some level he can't and never will be ok with it.
Dukat's fate in "Sacrifice of the Angels" is something I thought was different, really good, and crazy when I first watched it. Because I thought it was the end of the character, and that basically we had watched the character's entire ego be destroyed over the course of 40 minutes.
