I remember the good ol' days watching Star Trek: The Next Generation with my dad. Earliest I can remember was "The Child" (first time it premiered). Trek was sort of a family thing. Of course, the only non TNG Trek we saw was on New Year's day, when they would have marathons.
That become sort of a forgotten past time until I rented Star Trek: Generations (which, to this day, I do not understand why there is a great dislike for it.)
My favorite Episodes would have to be I Borg (after establishing the borg as this unflinching, unfeeling, brutal menace, they actually managed to humanize them), Time's Arrow (heh heh... Mark Twain), and Deja Q.
My favorite Character is Chief O'Brien, probably because he's proof that an overweight Irish dude can still end up with a cute asian girl (if I have offended anyone, get a sense of humor. I can go on a rant about Rosalind Chao. After all, I'm also a M*A*S*H fan).