Timecop very optimistically predicted the advancement from then-current 1994 technology to full-on time travel, including infrastructure and a regulatory and enforcement agency fully in place in just 10 years (it’s set in 2004).
Does the movie “The Day After Tomorrow” take place two days in the future? 
The disaster movie 2012 was released in 2009.
TCMF-2L
For an obvious example Star Wars was set in a galaxy a long time ago…
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The first X-Men movie was released in 2000. It takes place in the “not too distant future.”
Typed this on my phone. Please excuse any typos.
Snow Crash (1992) doesn’t give a date, except early 21st century. It won’t win this thread, but while I enjoyed it, the predictions were a bit implausible, especially the social changes. IIRC one character was around (adult?) during the Vietnam war. He appears digitally as ~50.
Nineteen Eighty-Four is all about blatant lies becoming truth. There is no reason to believe that it is actually 1984.
Boo, I came to say this. 2007 though, live version on the EP.
Lost in Space premiered in 1965, was supposedly set in 1997.
Not as close as Back to the Future, but still near future.
That’s nothing; Terminator 3 was #1 at the box office over Fourth of July weekend in 2003, and was set . . . later that very month!
Sweet!
Well, I did explicitly state in the OP that “SF set in the past or alternate present doesn’t count.” So yes, I know such works exist, and they’re not what I’m asking about.
I’m asking about one particular … trope? theme? seems a little to narrow to be a genre … of SF, wherein someone is concocting a future that could arise after their actual present.
And I’m mostly just interested in figuring out what SF is set in a very near future —Strange Days is a great example that I hadn’t thought of at all. It’s not intended to be a competition or an argument or anything other than a point of discussion.
Well, we’re all interested in the future. That is where we will spend the rest of our lives!
Well there’s 2001 a Space Odyssey, obviously. That was released in 1968, and postulated a vastly more advanced space program than we ever achieved. I’ll always remember how Pan Am owned the space plane that took the annoying first half lead character to the spaceport/space station.
Interesting how many of these examples seem to be in the 20-30–year range.
metrophage was set in an unspecified future but oddly enough 80- 90 percent of the book is happening today …
Of stuff I’ve seen recently Arrival seems to be set in a pretty well current time. I cant recall if the film sets a date, but the technology looks just modern.
The Irwin Allen “Time Tunnel” tv show was broadcast in 1966-67 and was set in 1968. His “Voyage to the Bottom of the Sea” was generally set a decade ahead, various years in the early 1970s are shown at the beginning of some episodes.
Next is a film about a protagonist who can see the future.
Well, he see’s two minutes into the future. 
(Yes, this preposterous premise does feature Nicholas Cage! How’d you guess? 
)
A good example of that is the TV showCentury City, which was made in 2004.
Picture a science fiction version of LA Law, and you’ve got it. The cases dealt with the legal and social implications of technologies that were then expected to be reasonably close to becoming real-world issues. Like, self-driving cars, genetic engineering, tracking devices for kids, things like that.
How about Flashforward, a novel they made a TV show out of (I didn’t finish the show because it got kinda boring, but I did read the book and there seems to have been significant changes in adaptation.) Written in 1999, set in 2009 at the activation of the Large Hadron Collider. People flash forward about two decades into the future. (The only reason for the novel to be set any time other than that of its publication was that the collider had to be completed.)
I don’t know how this fits exactly, but there was the late 90s TV show *Early Edition *(Kyle Chandler) that featured a guy who get’s tomorrow’s Chicago Sun-Times today and so he could deal with the future, in a limited way, as he wished.
So it was set today with an arriving tomorrow? or his tomorrow changed his today?
He had a cat that was on to it and a sidekick that wanted to make bets.
I certainly would’ve checked out the sports section.
And in a later episode, he runs across a guy from New York in the same situation, except that he does take advantage of the information to make money, and has a whole team of gophers doing rescues for him with no negative consequences, implying that it wasn’t outside the rules and Gary was being a stick in the mud.
(The series ended before 9/11, else they would have had some ‘splainin’ to do.)