"Sign Off" by Cliff Eidelman

For all the "Captain's Log" moments in Star Trek, this is probably the most memorable for me, because it's the last log entry for Captain Kirk and his crew, as they and Enterprise literally sail off into the sunset (or is that the second star to the right?). Kirk's log serves as a baton-passing to the crew of The Next Generation (the original draft of the log entry actually cited "a new generation"), and is the first time Kirk speaks the updated "boldly going...where no one has gone before" line.

Captain's log, stardate 9529.1. This is the final cruise of the starship Enterprise under my command. This ship and her history will shortly become the care of another crew. To them and their posterity will we commit our future. They will continue the voyages we have begun and join to all the undiscovered countries, boldly going where no manwhere no onehas gone before.
- Captain James T. Kirk

It also helps that the moment is (as is the rest of the film) beautifully scored by Cliff Eidelman. Initially somber as the crew realizes that their careers have run their course, Eidelman inserts a triumphant French horn playing of the Alexander Courage fanfare as a button on that immortal Spock response to Starfleet's orders to decomission Enterprise:

"If I were human, I believe my response would be, 'Go to hell,'...if I were human."

In that moment, the entire feeling of the cue changes. Instead of apprehension about the looming prospects of retirement, there is now a sense of peace as Eidelman plays his main heroic theme, which swells as Kirk gives the order to Chekov to head to the "second star to the right, and straight on 'til morning," and ultimately crescendos with the Courage fanfare once again.

This is then followed by an absolutely glorious playing of Eidelman's and Courage's themes over the cast signatures in one of my favorite send off moments ever in a film (one that was absolutely aped by Marvel for AVENGERS: ENDGAME, but then they can't be trusted to do anything original, can they?).