The one thing about STAR TREK that's changed my life is in the way that I look at entertainment. STAR WARS, for example, is a fairy tale about Good Vs. Evil and the only way it really stays with you over the years, is by way of nostalgia. And that's cool! I mean ... it's good that it can do that for people, but there's really nothing deep going on, here. It's not trying to be the answer to Kleenex, or anything, it just wants to entertain and that's all. STAR TREK, though, is something where you can watch it as a kid and it's really no different than STAR WARS in the sense of just being a space adventure story. But the fact that STAR TREK tends to be so topical means that as you indulge your nostalgia, later on, you pick up on things that you did not, before. The show was really "about" something else, entirely, so that now, it's not just about the kid you were, you can actually appreciate it as an adult, this time.
Well... Star Wars is supposed to be mythology in line with Joseph Campbell. And things like mythology/folklore, classical studies, archaeology, dead languages, etc. do not *need* to be topical. Those are things that you study purely for their own sake. They don't seek to offer some special insight on contemporary issues. And that's perfectly OK.
Kor
I think mythology "says" there are no contemporary issues. They are always the same issues and myth deals with or re-tells those same issues again and again with different specifics but the same archetypes, which are timeless. Our public dreams. Frankly I think this is why SW is more broadly popular than Trek. Though not with me.

To the point: Trek did not change my life, it is an important stream in forming me. Some ways, of course, I cannot be conscious of (since I began in a depth psychology way, above). To my knowledge, I believe that Trek helped teach me tolerance and humanity: don't kill the Gorn or the Horta! It also gave me heroes to emulate, much as comic movies do for kids today.