I never got into any STar Trek except the original and the movies (the newest is excellent in its portrayal of the young crew). But I think the show presented some very profound and thought-provoking moral issues - things that were pretty advanced for the time. I always like Miri for that reason, how it portrayed what might happen if a group of kids were abandoned and had to survive. A theme that was woven through so many episodes was the idea of good and evil existing within each of us. Plus so much of the technology was really predictive of things we now have.
Some other fave episodes: Tomorrow is Yesterday - where they travel back in time and are mistaken for a UFO, then accidentally pick up a fighter jet pilot. And who could forget Sulu's swordplay in The Naked Time. All Our Yesterdays - where they enter this time travel library and find Mariette Hartley exiled in an ice age cave.
Also love The Firm: http://www.youtube.com/watch?v=zhPiAFmYBDs "We come in peace, shoot to kill" "It's life, Jim, but not as we know it" "It's worse than that, he's dead, Jim"