I touched on this a bit in my novel Department of Temporal Investigations: Watching the Clock, when Claire Raymond (the 20th-century woman revived from cryogenic stasis in TNG: "The Neutral Zone") reflected on the SFTV of her era. I deduced that without the influence of Star Trek, science fiction would probably never have taken off in popular culture the way it did, and would've remained a disreputable niche genre seen as kids' stuff. Without ST, there might never have been a Star Wars, since Lucas used the success of Trek in syndication to convince studio execs that there was a market for space opera (and he obviously named it as an homage). And without TNG, who knows if the market for first-run syndicated hourlong dramas would ever have opened up?
In the book, I hinted that Quinn Martin's The Invaders was more prominent without the competition from ST, along with The Six Million Dollar Man and The Bionic Woman. While many genre shows would likely not have been made without ST’s influence, the bionic shows were based on a novel and were more along the lines of spy or superhero shows. Beyond that, though, once we get into the '70s or '80s, it's hard to say. It's possible that anime imports would've been more influential, filling the void in American genre TV, but on the other hand, I don't know if Star Blazers (Uchuu Senkan Yamato) or Battle of the Planets (Gatchaman) would ever have been imported to the US if it weren't for the desire to jump on the Star Wars bandwagon.
On the other hand, we might still have gotten the 1980 Flash Gordon, since that was an adaptation of a popular comic strip and movie serial hero. It was Lucas's failure to convince Dino De Laurentiis to let him direct the Flash Gordon movie that led him to create Star Wars instead. So maybe Lucas would've still gotten to make a form of that movie eventually, but whether it would've been as revolutionary is hard to say. Although Steven Spielberg was as important to the 1980s FX-driven blockbuster revolution as Lucas was.
Without Star Trek to offer an optimistic vision of the future, SFTV and film might have remained dominated by dystopias and post-apocalyptic narratives, and the popular culture may have been darker as a result. Who knows? Maybe that pessimism about the future is the reason they had the nigh-apocalyptic Eugenics Wars and then WWIII.