Besides Star Trek, what other 'future' Earth movies have an optimistic view? If I was asking about distopian futures you could fill volumes. But I have a hard time thinking of too many 'good' futures. Do they feel good sci-fi can only come from bleak futures?
2001: A Space Odyssey certainly does not depict a dystopia. Though I must admit I'm often drawn to more cynical fare, and am somewhat blanking at the moment.
That's obviously not how the question was meant. Optimistic, positive views of the future aren't very common either in film or prose science fiction. This is partly because stories are about conflict and crises; it's not easy to tell an exciting or dramatic story set in a wonderful, happy world. But it's not all dystopias. Back to the Future Part II showed a 2015 that was neither better nor worse than the world we know; it had its problems but it also had improvements. Minority Report was in a future that seemed pretty prosperous, clean, and upbeat, aside from the ethical dilemmas of the Precrime program (and the annoying, ubiquitous ads that addressed you by name). The Bicentennial Man showed a fairly positive future, though one with oddly limited technological progress. I'm sure there are others.
I don't know if I'd characterize Minority Report as particularly optimistic. Besides the predictably happy and neat ending (this is Spielberg, after all), I don't think the film postulated we had changed much as a society, unlike Star Trek. People still had affairs, still committed murder (both murders of passion and murders that were pre-mediated), people were still exploited (the Pre-Cogs), people still lived in poverty (the slums Anderton hides out in after his eye operation, speaking of which there was still a need for black market surgeons dealing with organs of dubious origin, and to top it all off, the movie portrayed advertising as far, far more insidious than it is today. Most of the 'optimistic' changes were aesthetic, and not really for the better. If you want a Spielberg film that is more optimistic in its message, try Close Encounters of the Third Kind, although that was set in the then present day and not in the future.
^My point is that it wasn't a dystopia. Of course it had its problems; any society would. But it looked like it wouldn't have been a bad place to live so long as you were a law-abiding citizen with a decent job.
It doesn't actually show much of future society, but if you like Star Trek, you should watch Forbidden Planet. Also, while Babylon 5 takes place in an imperfect world, I find it to have a very optimistic tone. 2001 and 2010, thought technically in an alternate past now (neo-Steampunk ) are both pretty optimistic.
An advert for Pre-Crime within the movie claimed that the murder rate in the US had reached "epidemic proportions", whatever that means. That doesn't seem too optimistic.
It also sounds like typical politcal hyperbole. Which doesn't sound optimistic, either, but it's one reason note to take that bit at face value.
The book 2010 was pretty optimistic, but the movie was quite pessimistic, depicting an Earth on the brink of nuclear war and needing alien intervention, essentially, to knock some sense into humanity. Clarke's novel showed American and Soviet astronauts who got along excellently, reflecting the real-life amity between scientists from the two powers, but Peter Hyams tried to make the film more "topical" by throwing in a lot of Cold War tension, which just ended up dating the film badly when the Soviet Union fell just half a decade later. Again, my point was only that it wasn't a dystopia. How many times do I have to say that? I wasn't claiming my examples depicted especially optimistic or utopian futures; I was merely offering them as counterexamples to the OP's observation that most cinematic futures are bleak and hopeless. A future that's no worse than the present does count as an example of a non-dystopian future. (Unless you believe that the present constitutes a dystopia.) As I recall, that ad for Precrime referred to the murder rate before the program was instituted, not at the time of the film. Of course, with the program ending at the close of the film, it's possible that the murder rate would skyrocket again, in which case you'd have a point.
That's the heart of the problem. A story requires conflict, problems to solve, and a utopian future is broadly defined by an absence of such problems. One of the big problems with utopian fiction in centuries past is that they were really treatises of philosophy and political economy rather than stories per se, really boring in most cases, and the same problem will carry over to film. Add to that the fact that were currently in a period focused on bleakness, as the success of things like nuBSG prompts everybody and their uncle to ape the tone whether doing so is correct for the setting or not, plus the problems in defining optimistic (ALIEN and its sequels, for instance, don't show a future particularly worse than the present, but no-one would call it positive because of the focus and mood), and there isn't much out there. Trek was really the rare exception in that it used to be both optimistic and engaging, until it too got shoved onto the death and devastation bandwagon. Maybe terminology could help here. Some have proposed the idea of a "heterotopia", a future society that is neither particularly dystopian or particularly utopain. Others have called the term redundant, because no utopian story will lack a problem to propel the plot, and few dystopian stories an attempt at resistance or room for happiness amidst the negativity, but I think it works it the narrower sense of a future designed to be balanced between the positive and the negative. So a lot of societies from sci-fi films, like Minority Report or I, Robot or even Riddick (Helion Prime was a prosperous, diverse society) could qualify as heterotopian, even if the immediate focus of the plot is on one aspect that is more dystopian than the norm. I suppose that depends on scale. Looking only at modern western socities you could truthfully call the present heterotopian--there are persistent problems of health, poverty and crime for some segments of the society but much prosperity and opportunity more generally. From a global perspective, though, with wealth concentrated in a fraction of the population, war, disease, ignorance and oppression, I'd certainly call the present a dystopia. Fictitiously yours, Trent Roman