Ps. I come in peace. My intention is not to insult any Trekkies out there, I mean only to learn why so many people adore the series.
Then, and I mean this gently, go start a new thread about that. Don't disrupt this thread to ask a barely related question. While I have some things to say, I won't help you disrupt this thread to answer it. (I know you meant no harm, which is why I am trying to be nice)
Anyway, since you didn't restrict it to official series, I will have to say that "World Enough and Time" from New Voyages may be my new favorite, although I haven't seen much of the official series in a while. George Takei gives one of his best performances, and the story is quite touching in that classic Star Trek way.
As for the official series, two of my favorites are both from DS9, but I don't remember their titles. Actually, thanks to wikipedia and Memory Alpha, I found that name of one, "The begotten," but can't find the other, the one where they find a planet settled by their descendants.