It really is astonishing, and easy to forget how unusual it is, just how long a run Trek had for this.
People sometimes talk about the continuity like it's utter fail but it's been a very well done universe full of attention to detail, shout outs to other series and obvious effort put in to be faithful to what's been established as well as build on it.
Initially...Janeway, EMH, Kes, Seven. Later, everyone. Yes, even TNG. And Bill Ware Theiss costume design (heaven!) and TOS production design and lighting (so much with so little). Passion. Drama. Sex. Humour (lots of it). Even the technobabble can be occasionally sexy. The allegories/metaphors?...not so much... I LOVE the way the movies made the TOS TV crew even larger-than-life. Kirk et al finally found their perfect medium (as JJ has proved). T'Pol.
Oh that is such a good way of putting it, the TOS movies really did make them larger than life! I think that's part of what attracts me to the TOS movies. They're clunky but they all about the Big Three in a Big Way!
All of the above, and add the NCC-1701, the refit, and the -A. The JJ Enterprise ain't no slouch, either.
Since I'm the one who's been shitting on Trek's continuity recently, I should point out that they DO create a very good illusion of everything taking place in one big universe (so long as you don't look too closely) and spotting all the references and callbacks is one of my favourite things about Trek.
The one thing I've always been aware of is what STAR TREK means to people. I'm not even sure what it means to me ... why I love it, so much. I suspect that it's because it's always been there, partly. But mostly, because of the optomism. Even when it's necessary that someone dies in STAR TREK - a star wants to leave the show, etc. - there's some uptick to it, to ensure that hope lives on. For example, Yar gets killed in TNG, which sucks. We're not getting her back ... Denise Crosby's going onto other things. BUT ... Yar gets a funeral where her hologram message to her friends, not to be manipulating, but to restore a sense of hope to the proceedings. And STAR TREK, in general, has given a lot of people not just entertainment but hope. Hope that these ideas that we're seeing of people who accept eachother and work together in peace for mutual advantage and understanding are shared by other people calling themselves fans of the show. And just the fact that STAR TREK genuinely wants to entertain, I think. That always speaks to me.