Improvisation can be the best friend of some directors and the bane of some others' lives. The entire premise means that the crew won't know what's coming, which can be a very stressful situation to be in. On the other hand, when the cast know the characters so well as to be able to take control, it can work entirely for the best.
Leonard Nimoy was the first and last stop for all things Spock, so the moments that feature him on this list should come as no surprise. There has been a lot of silliness through the years as well, with Aron Eisenberg bringing his goofy nature to the set when asked.
It's not always the actors who can take credit for improvisation either. Even when the script is shooting, there can be changes made on the fly to scenes if the writers or directors think it's best, with a couple of examples here proving that this really can deliver the goods.
And, at the end of the day, if you're going to cast a comic, just let the comic do the talking.
10. The Vulcan Neck Pinch - The Enemy Within
The original script written by Richard Matheson directed that Spock 'kayoed' the evil Kirk, which effectively meant that the Vulcan had to punch the man so hard he fell unconscious. While Vulcan strength had clearly been depicted and Spock would have been well capable of doing so, Leonard Nimoy objected to the scene. He felt that a Vulcan of such restraint and calibre would find a more dignified way to incapacitate Kirk.
He devised the neck pinch and worked with William Shatner to perfect it before they brought it to director Leo Penn. All agreed that it was a better fit for the episode, and another Vulcan tradition was born at that moment.
Since this moment, the neck pinch has appeared many times in Star Trek, performed by several different characters. Data performs it on Commander Sela, while Picard performs it on a space pirate - one who happens to be played by future Tuvok actor Tim Russ. It is now almost as iconic as the Vulcan salute itself, which has its own creation owed to a certain Mr. Nimoy as well.