Great question. Something I have thought about myself.
I look at Laurel and Hardy movies, and love them, but realize that very few in this generation know who those guys were. For the most part, they will be forgotten.
I think it is up to us really, up to
our generation to pass it on. We must continue to make comments, videos, art, music, and stories that revolve around it.
The internet age is unprecedented in human history, which I think may help the process. The
real reason I think it should be kept alive because most of us
want that utopian future where the betterment of mankind (as a collective) is the most important thing, not money. Where everyone is equal and humanity is living an amazing adventure of exploration and discovery.
It is like a myth that must be kept alive until we achieve its ends.

Spockboy
The problem with the bolded part is that the only person in the whole Federation who thinks nobody cares about money is Jean-Luc Picard.
Beverly didn't get her bolt of cloth for free. Ro had to remind Picard that if he was pretending to pick up a prostitute, he had to be seen to pay her. The economy of DS9 ran on gold-pressed latinum. The economy of Voyager ran on the barter system (when trading with various planets and alien ships), replicator rations, and holodeck time. I'm fairly sure that Robert Picard and Ben Sisko's father aren't running the winery and restaurant just for fun - they need to make a profit or they'd go out of business.
And Kirk telling Gillian that they don't use money in the 23rd century? What he actually meant was that they don't use
cash. He didn't offer to pay for the pizza for several reasons: 1. Gillian was the one who invited him, so it was her duty to pay; 2. Kirk only got $100 for his glasses, which he divvied up among the crew. He wouldn't have had enough to pay for the pizza anyway; 3. As a non-cash-carrying member of Starfleet, Kirk would have been accustomed to an electronic banking system where a voiceprint or some other identifier would have been all that was necessary to facilitate a transfer of funds. Obviously he wouldn't have had access to that 300 years in the past.
Even now, many people are so used to debit and credit cards that they rarely carry much cash. Even the need to keep a few coins on hand for a pay phone meets with upraised eyebrows, because the pay phone just doesn't exist the way it used to, at least around here. The coffee shop where I had lunch yesterday only requires that the bill be at least $3.00 to accept debit/credit card payments.
Of course they (we) will go almost extinct. And that's ok. The vast majority of my HS students have never seen an ep. Some saw the recent movies that came and went like many others. Just like one of the Thors or Avengers. Ephemera.
Somebody mentions Shakespeare upthread and how fine he's doing. Um. My students read one play (Macbeth - arguably the most accessible) and hate it. One girl called it gibberish. I don't think he's doing fine. More 'n half of Americans don't read a book, so I don't think ol' Will's doing that great.
He's doing just fine in places where people do read.
Macbeth is the "most accessible" Shakespeare play? Really? It's the only one I ever saw performed live where I nearly fell asleep from boredom. Maybe I need to study it better, or maybe the theatre company needed better actors. All I know is that it was much more interesting to read than it was to watch.
I'd have thought high school kids could best relate to Romeo and Juliet. After all, the protagonists are kids of high school age, going through that first-love thing that so many young teens have gone through for millennia. Of course I do get that modern kids probably can't relate to the reasons why Romeo & Juliet did what they did (secret marriage before going to bed, for example; not too many kids would worry about that nowadays).
Shakespeare was meant to be seen and heard, not read. Yeah, a person can read a Shakespeare play and enjoy it (I have), but it only really comes to life when it's
performed. If high schools are going to continue to teach Shakespeare, they really should include at least one live performance in the curriculum - even if it's a movie like
Romeo and Juliet,
Hamlet,
Twelfth Night,
Much Ado About Nothing, or
Henry V (just listing my favorites; even my grandmother loved the Branagh version of
Henry V and she'd never read Shakespeare or seen a live Shakespeare play in her life).
It's arrogant really to want 2015 to embrace what I/we happened to in the 70s or 90s.
Why arrogant? I'm sure the people who were Shakespeare fans 400 years ago would be glad to know that people centuries in the future shared their interest.
In the meantime, why not try out some of the fan films? Some of them are excellent at recreating the look and feel of the actual TV series, and they have good, entertaining stories.
Two of them are good, the rest are okay, but they should not be a complete replacement for the official productions that are on the big screen now.
As far as I'm concerned, they are a more than adequate replacement for nuTrek. Sure, I may privately think that Phase II's version of Peter Kirk needs a haircut, but the stories themselves are enjoyable. Some of the Phase II material had me in tears, and I have to compliment the people on those productions for eliciting such a reaction. I'm not normally a sentimental person like that unless a dog or cat is involved. And I enjoy all the Star Trek Continues films, from the episodes to the vignettes to the parody of "Shatner on the Mount."
If other people like nuTrek, they are welcome to do so. I don't like it, so I'm thankful that there are creative and talented people willing to make entertaining fan films.
Hopefully so.
I mean, every generation has their thing. We tend to look back on past generations as if they had no life because they had no cell phone or Lady Gaga, but they had a culture and a life too, and I guarantee they weren't spending much of their life worrying that we were missing out on the cultural icon of Shakespeare, or the richness of the renaissance. Actually, I find the idea of Star Trek (in its current form, anyway) being a phenomenon 100 years from now a bit concerning. That would almost imply that creativity had stagnated.
Again, using Shakespeare as a reference... has our creativity stagnated because people still like Shakespeare? I don't think so. It provides inspiration for many other creative endeavors - musical theatre, for example. "West Side Story" is still a powerful play. And how many Shakespeare references are there among the various Star Trek series and movies? I haven't counted them myself, but I know there are more than a few.