I'm not sure it has a real chance (can sf fandom's mixed reaction to Dicovery compete with its love of Black Mirror?), but it caused me to journey back in time and take a look at how often Star Trek has competed for and/or won a Hugo Award.
Before Star Trek (1958-66)First, a little context. Though the Hugo Award for Best Dramatic Presentation (i.e., usually a film or tv episode, though plays and albums and such have been finalists as well) was first awarded in 1958, its early years were pretty rocky. In some years (1964 and 1966) the category just didn't exist; World Science Fiction Convention organizing committees have the latitude to cancel any category where the nominations are paltry in number. In other years pre-Star Trek, the category was won by No Award; Hugo voters thought it was better for nothing to win the award in 1963 than for Night of the Eagle to win it.
In 1965, the last award year before Star Trek was a Hugo finalist, there were just two finalists, instead of the usual five: Dr. Strangelove and 7 Faces of Dr. Lao. (Strangelove won, of course.) I bring all this up to show what minimal options there were for quality sf on screen before Star Trek arrived on the scene.
The Heyday of the Original Series (1967-71)1967, Star Trek was first eligible for the Hugo Award. Even though only fourteen Star Trek stories were broadcast in 1966, three of them were finalists, which is an excellent success rate. They were "The Naked Time," "The Corbomite Maneuver," and "The Menagerie" (the whole two-parter as one). It's sort of an odd bunch: I don't think anyone now would look back on any of these as classics. The first half of Star Trek's first season is good, but not great, but had I been a Hugo voter in 1967, I'd've nominated "Balance of Terror," one of Star Trek's all-time bests. The category was won by "The Menagerie," also beating out the film adaptations of Fantastic Voyage and Fahrenheit 451. I do think that of the three, that's the one I'd go with, and it definitely demonstrates fans' preference for mythology-bending episodes.
1968, when all five finalists were episodes of Star Trek: "The City on the Edge of Forever," "Amok Time," "Mirror, Mirror," "The Doomsday Machine," and "The Trouble with Tribbles."* These are all excellent episodes; the second half of season 1 and the first half of season 2 really is one of Star Trek's best periods. The only quibble I would make is that I think "The Devil in the Dark" deserves to be in there, perhaps instead of "Amok Time." The category was of course won by "City on the Edge."
In addition, the transcript of the Hugo Awards ceremony for 1968 indicates that Gene Roddenberry was present, and the organizing committee gave him a special plaque inscribed "for producing Star Trek." So you can see what an effect Star Trek was having on sf fandom in the 1960s!
Star Trek's domination ended quickly, however. Late season 2 was when the rot set in, and not a single episode of Star Trek ended up on the ballot for 1969. I would have nominated "A Piece of the Action" (i.e., the gangster one) myself, but then, I'm weird. The finalists that year were 2001: A Space Odyssey, Charly, The Prisoner: "Fall Out," Rosemary's Baby, and Yellow Submarine. Of course 2001 won. Hard to argue with that. Nothing was a finalist in 1970, either, the year infamously won by news coverage of the Apollo 11 landing.
And with Star Trek gone, the category settled into its previous rut, with No Award beating out all five finalists in 1971, and again in 1977.†
Star Trek on Film (1980-87)
The Motion Picture lost out to Alien in 1980, though it did come in above The Muppet Movie (which it did not occur to me to categorize as sf) and The Black Hole (which came in below No Award). This seems justifiable to me.
1983, which again, seems justifiable. It did beat E.T., The Dark Crystal, and first Mad Max film.
The Search for Spock came in third place to 2010: The Year We Make Contact in 1985, which is a goddamn travesty if you ask me. 2010 is a poor film with a couple good parts; Search for Spock is a decent movie, with a couple excellent parts. (I think its problem is that it climaxes early; stealing the Enterprise is clearly the best part of the film, meaning everything after that kind of drags.) It wasn't a very good year for sf on film, actually, with the other finalists being Ghostbusters, Dune, and The Last Starfighter. I probably would have voted for Ghostbusters.
In 1987, Star Trek again lost to the Alien franchise, when The Voyage Home came in second to Aliens. I would vote for Voyage Home, personally, but I can see it.
The Heyday of The Next Generation (1988-95)In 1987, Star Trek: The Next Generation debuted; in 1988, television Star Trek returned to the Hugo ballot. Alas, however, the best TNG could do was "Encounter at Farpoint." Even though it's not very good, I don't think I can disagree that "Farpoint" is the best TNG episode of 1987; the first season is mostly shit. "Farpoint" came in third, losing to The Princess Bride. Not exactly inconceivable.
In 1989, The Final Frontier became the first Star Trek film to fail to make the ballot. Well, duh. (Who Framed Roger Rabbit? went on to win.) 1989 is a rare pre-2001 Worldcon from which nominating data still exists. That year, it took at least 58 nominations to make it onto the ballot for Best Dramatic Presentation. The TNG episode "Elementary, Dear Data" received 15; if The Final Frontier received any, it was below 12 and therefore the threshold for being listed in the detailed breakdown. The Land Before Time got more nominations than either!
Things returned to normal in 1992, when The Undiscovered Country made the ballot. It, however, came in third, losing out to Terminator 2 and The Beauty and the Beast. Ouch.
The Next Generation made the ballot again in 1993, when the classic episode "The Inner Light" not only was a finalist, but won the category, giving Star Trek its first win in twenty-five years. Nice! The other finalists from that year are pretty dreadful, though (they include Batman Returns and Alien 3), so there you go. (Did you know? I've actually never seen "Inner Light"! But people say it's a good one.)
And then in 1995, Star Trek had multiple finalists for the first time since 1968, when both the TNG series finale, "All Good Things...", and the first TNG film, Generations, made the ballot. "All Good Things" won, garnering Star Trek its fourth win-- and, not to give the game away, final win to date. Another deserved victory; I'd definitely give it to "All Good Things" over The Mask or Stargate.
Always the Tawi'Yan, Never the Groom (1996-2002)1996, "The Visitor" was the first episode of Deep Space Nine to make the ballot, though it lost to an episode of Babylon 5.
In 1997, Star Trek once again garnered a double ballot appearance, with First Contact and Deep Space Nine: "Trials and Tribble-ations." They came in second and third, respectively, but were beat out by another episode of Bablyon 5. And, in fact, they could not have both made the ballot if J. Michael Straczynski had not declined nomination for three other episodes of Babylon 5 that met the nomination threshold that year!
As a side note, a Hugo Award actually appeared on the show in 1998. In the 1953-set DS9 episode "Far Beyond the Stars," the one of the episode's various sf writer characters walks by carrying a Hugo Award in his hands:
Memory Alpha indicates the award wasn't actually one of the ones won by Star Trek. It was one of two won by production illustrator Rick Sternbach, back in 1977 and 1978, for Best Professional Artist. Given the first Hugo Awards were given in 1953, the character must have won that very year. The appearance of the award itself is anachronistic; the award's appearance fluctuated throughout its first few decades, and in 1953 it actually looked like this, not as sleek as the design that was eventually adopted.
1999, maybe just out of sheer inertia. It came in last, losing to The Truman Show, Dark City, Pleasantville, and another damn Babylon 5 episode. I'd definitely give it to Truman Show too.
Star Trek: Voyager went off the air in 2001. It is the only live-action Star Trek series to never be a Hugo finalist.
The Split (2003-06)Contrary to the situation in the 1960s, by the 2000s, we were flooded with quality sf on screen. With that in mind, in 2003, Worldcon split the Best Dramatic Presentation award into two separate categories, "long form" and "short form." The cut-off is ninety minutes, which lets two-part episodes be nominated as one under short form, but places films and entire seasons of television programs under long form.
Star Trek was also eligible in long form that year, but Nemesis failed to make the ballot by a wide margin; the minimum required was 130 nominations, and Nemesis received only 43. It did, however, get more nominations than Signs or Solaris, both of which are much better films. (The Two Towers won.)
Enterprise never made the ballot again, which is a shame, because the show actually got good at that point. (Notoriously, 2004 was the year the short form category was won by a three-minute clip of Andy Serkis and Gollum accepting the MTV Movie Award for Best Animated Performance. But if you look at the other four finalists from that year, it actually is the best thing on the ballot. I probably would have voted for No Award.)
State of Decay (2006-17)Once Enterprise went off the air in 2005, there was no Star Trek eligible to be a Hugo finalist until J. J. Abrams's 2009 Star Trek film.
2008, a Star Trek fanfilm made the final ballot. The episode "World Enough and Time" of New Voyages garnered 48 nominations. I haven't seen it, I'm told it really is good, but every episode of New Voyages (later rebranded Phase II) I have seen has been execrable. That's more nominations than episodes of Battlestar Galactica, Torchwood, Pushing Daisies, Lost, and Stargate SG-1. I seem to recall a lot of people being mad about this, thinking it not right that a fanfilm should be Hugo finalist, but upon doing some Googling, maybe I'm confusing it with the fact that "World Enough and Time" was also a Nebula finalist. Unlike the Hugos, the Nebula rules specify finalists must be professionally produced, and that's clearly untrue of a fan film.
In any case, "World Enough and Time" came in last. Doctor Who: "Blink" was on the ballot that year, so there really was no question what would win.
2010, Abrams's Star Trek was the last Star Trek film to land on the Hugo ballot. It came in fourth, losing to Moon, District 9, and Up, but beating Avatar. That seems entirely reasonable.
That was it for Star Trek until this year. Star Trek Into Darkness didn't make the ballot in 2014 (138 nominations were required; it got 88), and neither did Star Trek Beyond in 2017 (240 nominations required; it received 113). That latter is a shame, at least; I'd've ranked Beyond above some of the actual finalists, like the Ghostbusters reboot, Deadpool, and Rogue One.
The Future (2018-??)Like I said, I don't expect Discovery to win this year, even though I ranked it first myself. I'm pretty sure it will be Black Mirror's "USS Callister." I don't know if a hypothetical fourth reboot film will get back on the ballot, either.
In some ways, though, Star Trek is a victim of its own success. Before Star Trek, there was often not enough sf on screen to even merit giving an award for it. Since Star Trek (and, admittedly, Star Wars), we've been flooded with sf on screen. Mediocre Star Trek films used to make the ballot regularly; now even good ones can't push their way in. It's a good problem to have as an sf fan, but a sad one as Star Trek fan.
* This couldn't happen these days. In part as a reaction to the dominance of Doctor Who (which claimed three of five finalist slots in 2006, 2007, 2008, 2010, 2011, 2012, and 2013), in 2017 a new rule went into effect: "No author, or group of authors, or dramatic presentation series, can have more than two finalists in any one category."
† 1977 would be the last time any Hugo category was won by No Award until 2015 (when No Award was used to counter the effects of slating). According to Kevin Standlee, "There has been speculation that Star Wars [A New Hope], which had just premiered and would go on to win the 1978 Hugo Award, had had such an effect upon the voters that they rejected all of the 1977 Hugo Award finalists by comparison, even though Star Wars was not eligible for the 1977 Awards."