In all of the televised episodes of Star Trek (TOS, TAS, TNG, DS9, VOY & ENT), what was the single highest Nielsen rated episode?
The series premiere for TOS (The Man Trap) opened with a Nielsen rating of 25.2 (albeit facing dramatically less competition than future shows). This is a figure that would never again be matched by any trek episode.
The series premiere DS9 (Emissary) garnered the largest overall Nielsen rating for a modern show with a score of 18.8.
The next most popular was the series finale of TNG (All Good Things) with a score of 17.4
The highest rated episode of Voyager was the series premiere (Caretaker) with a score of 13.3.
You can see the Nielsen ratings for ALL modern Star Trek episodes (TNG, DS9, VOY, and ENT) plotted together on this handy graph from here:
Which confirms Richard's answer (the highest outside of TOS is the DS9 premiere Emissary, followed by the TNG finale All Good Things), but I thought it was worth a separate answer for the complete graph displaying them all so nicely.