I'm ruling out Titanic. Really, all that it did was fire Leo through the ceiling for teenage girls. 80's and 90's babies still love Leo because it was ingrained in them when Titanic came out. Sure, it was a huge flick, but it wasn't the first tragedy movie, and it didn't really change the way that films were made.
I'll also say that T2, while it was great, wasn't as influential as we would think. Yes, the special effects were seemingly groundbreaking, but in terms of action films, this is more of the apex of that hyper-masculine era of the mid 80's through mid 90's. T1 (obviously) influenced T2, and T2's influence had run its course in Hollywood by the late 90's. Matrix took the torch from there, as far as influencing the action genre.
The Blair Witch Project changed the way that a lot of movies are made. It made low-budget acceptable and cool (not that horror hadn't done low budget to success before). However, it also ushered in the camcorder/FPV of horror. How many times has a movie been marketed on "found footage" or "based on real events" since then? It's almost the norm.
The Sixth Sense changed the way a lot of "horror" movies were made as well, IMO. It took the genre from just being scary to be scary to "these ghosts are scaring me/us, but WHY?" Even today, there is always a creepy ghost for half the movie, then it turns out that the creepy ghost is just trying to get some message across, so they show the main character how they were wronged, and the main character frees them, or somehow rights the wrong. The Sixth Sense made it important to add reasoning to the horror, or apply some "twist" at the end that the ghost wasn't all that bad, it was some other spirit or force.
If there's no Boyz N The Hood, then there's no Juice, Menace II Society, Friday, which were all influential in their own right.
This one could be a stretch, but what about the Star Wars remakes? I think that they made it ok to reboot or re-release movies or whole series. Think about how often Hollywood revisits the same movies to touch them up and release them again since then. Like I said, it's kind of a stretch, but they made it ok for Hollywood to say "Yeah we did it before, but let's cash in on it again!"
After reading the other responses and looking into it, I'll say Toy Story is the best answer. It really did change everything. Pulp Fiction is another great choice, but I think in terms of influence, nothing is touching TS.
I forgot about the blair witch project. it was more influential than scream tbh. It birthed that whole first person camcorder horror movie genre that is STILL popular today.
