1990, I was born in the midst of this generation Y. Do I think Harry Potter or Lord of the Rings or Prequel Star Wars are my generation's Star Wars? NO! The Prequels are the horrid offspring of what the previous generation created. There are way better candidates. Besides, I don't want to think of my idea as This Generations "Star Wars" but more of This Generation's "Cultural Phenomenon." And Prequels doesn't qualify.
Harry Potter could work but I argue Lord of the Rings works better. Why? Yes, the books predate Star Wars, but you damned yourself Chris with a point you made. Dungeons & Dragons was based off of Lord of the Rings and it's world. D&D was created in the 80's (ish) and continues to have a strong following. We also have the movies as well. But I argue there are better examples of Cultural Phenomenons for my generation. here are some of them with brief reasons why:
Alien (series)... and by extension, Predator - This is probably my number one choice because it was released in the early 80's. It had comics and crossover comics with DC and Marvel (i think). It spawned videogames with Alien vs. Predator. It made more movies with Alien vs. Predator. Not only that, but you will hear numerous references to Aliens in a number of games and other movies. And if anything other than a film series can be used as our cultural phenomenon, it'd be games.
Toy Story (series) - A little closer to my agegroup, but we'll see what the masses think. The human character, Andy, and I grew up at pretty much the same rate. When he was a kid playing with his toys, so was I. When he went off to college, so did I. This was Pixar's premier film, essentially, and it allowed them to make many more amazing films. The story is amazing. It's the best trilogy ever (or one of the best ever). I'd say this is another excellent candidate.
Back to the Future - Speaking of amazing trilogies! BttF is another great trilogy that was released in the mid-late 80's that many people still go back and watch because of how great it was. Arguably, not as big a boom as Star Wars or the other two I mentioned, but another noteworthy candidate.
Terminator - Released in the 80's and 90's the Terminator series is another big one that people loved. It is referenced and parodied quite often. Not to mention it is probably one of the few things in Schwarzenegger's career he can look back on without feeling any guilt.
If you have to choose a Generation Y Cultural Phenomenon, please make it one of these. Harry Potter and Lord of the Rings are so far off target.