Star Trek III: The Search for Spock ends with exactly this phrase as the end caption; it is effectively the Trope Namer, and possible inspiration for the Justice League Unlimited quote.
Kirk: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 journey to all the undiscovered countries, boldly going where no man, where no one, has gone before.
Star Trek: Generations ends with Picard telling Riker he believes there will be more ships named Enterprise.
The deleted final scene of Star Trek: Nemesis ends with the Enterprise repaired, and Captain Picard ordering that it be taken out once more to a system "where no one has been before."
Star Trek Into Darkness: Or rather, the adventure begins, with the film ending as the Enterprise leaves Earth to begin its five-year deep space exploration mission, which was the basis for the original series.
Star Trek Beyond ends with our heroes setting off in the newly-constructed Enterprise-A.
