Okay, I'll specify from the start that these aren't the "best" pieces of media, nor necessarily my favourite, but if I'm choosing media that shaped me, I can nominate:
A Song of Ice and Fire/Game of Thrones
As in, both the book and the TV show simultaniously shifted my standards for fantasy. Before that, throw together orcs, elves, and dwarfs, and I could probably be entertained. Post-GoT, a lot of fantasy has become very rote for me, relying on tropes that now feel tired. It's probably why I haven't been able to get into stuff like Shannara and Wheel of Time, and why stuff I was once enamored with (e.g. Warcraft) doesn't do it for me as much anymore. Also, with my own writing, GoT did shift my style noticably.
Battlestar Galactica (reboot)
Sort of. Maybe. Looking back a decade (good grief, it's been that long), Battlestar Galactica kind of did to sci-fi (for me) what GoT did for fantasy, though not nearly as impactful. The main way BSG changed me was its emphasis on episode-to-episode continuity, whereas for me, that was somewhat novel. Yes, other TV shows did it first (e.g Babylon 5), but at the time, that did change things for me. It probably shifted my tastes to some extent, though episode-to-episode continuity has pretty much become the default in sci-fi these days regardless. Even Star Trek went that route.
The Expanse
This is similar to BSG in a sense. Now, anyone who's read my reviews of these books will know that I have mixed feelings on the series. However, I say it shaped me because the series has an emphasis on hard sci-fi, and weaves that commitment to realism into its narrative. As such, it kind of shifted my expectations of how space-based fiction should function, even if settings use softer sci-fi. It affected me in the sense that in my own writing, I started using terminology lifted from the books (hard burns, tightbeams, etc.)
Halo
This is debatable, but I'm including it because Halo was the IP that really got me into exploring EU fiction. Yes, EU fiction existed well before Halo, and I'd even read some of it, but Halo was the one that kind of shifted my mindset to actively seeking EU fiction out for various settings. Also helped that the first Halo EU book remains the best in the series so far IMO.
Heroes of the Storm
This is the game that got me into MOBAs (well, sort of, it's the only MOBA I like, so does that count), but I'm not including it because of that. It's because of HotS that my gaming habits now include setting time aside for multiplayer-only stuff, whereas previously, I wouldn't have bothered. Now, on average, I still prefer singleplayer content, but playing HotS shifted my habits in this sense.
Metal Gear Solid/Legend of Zelda: Ocarina of Time/StarCraft
I'm including these three together because each of them represents a shift for me in my playing habits, and each of them were released in 1998. I can't recall which I played first (I think OoT?), but as a trifecta that came out in close proximity, I'm including them because each of these games has a strong narrative element that, for me, was pretty new. Yes, games with stories obviously existed well before these, but on the personal level...well, I'll put it this way. I grew up with Sonic (more on that later), and one time at the dinner table, little Hawki says that he had to play STH1 to beat Robotnik, as part of an act of infusing narrative to a game that technically didn't have any. As in, little me was taking what narrative he could find in games. Come 1998, this changed, in that I was exposed to games that could give me narrative on their own terms.
Lord of the Rings
I'm actually specifying the film trilogy here, because while I do respect the books, they don't make for easy reading material, and suffer a lot of bloat. But I'm including these because even now, the trilogy remains my favourite film(s) of all time (at least the extended editions do), and while I was exposed to big, blockbuster trilogies before that (e.g. the Star Wars re-release in the 90s, which was my first exposure to it), Lord of the Rings did kickstart a mania for me in collecting whatever LotR stuff I could - the tabletop wargame? Check. Movie tie-in works? Check. The books? Check. Videogames? Check. Heck, it's even created the only MMO I ever enjoyed playing. Lord of the Rings did shift my fantasy standards over a decade before Game of Thrones did, and it's why LotR doesn't feel trite to me in the same way that so many other fantasy settings now do thanks to GoT. Because LotR had that impact on me in the same way that GoT did.
Red vs. Blue
I'm including this because while RvB went to hell by season 9, if not earlier, it did shape my interests for awhile in that for a time, I actively sought out other machinima as a result.
Sonic the Hedgehog
This is a bit debatable, because if we're talking about shaping influences, then I'm not sure if this counts. I mean, it had a huge influence on me, growing up through the 90s (STH 2 on the Master System was the first videogame I ever played after all), but...actually, that might be reason enough. Because if I wasn't exposed to Sonic by chance at a friend's house that day, what would have changed for me? Arguably things would have changed for the better, I dunno, but whatever, it did shape me.
Sonic's arguably also a predecessor to Halo shaping me in that the games introduced me to the wider world of the setting, with the books and more importantly, the comics. I can't count these as EU in the same way that Halo can, but the Archie comics were the only comic subscription I ever had, and it was a subscriptio that lasted well over a decade, and while Sonic's fallen on hard times now, let me assure you, he was big in the 90s, and even people who took Nintendo's side in the console wars recognised that. So, I'm counting him.
Final Note
Again, these are the works that influenced me, not the ones that are the "best." Like, my favouite novel of all time is Brave New World, and 1984 ranks close, but while these are seminal works, I can't say they shaped my taste in media. Left an emotional and intellectual impact? Sure. Shaped my tastes? Not so much. I mean, they got me to try Farenheit 451, but I don't think that's in their league, so...