I'm not a game developer, so I can't say any of the following were super important for the industry as a whole, but...
Intro/title card for Ocarina of Time. Seeing a full grown, 3D Link riding across Hyrule Field on Epona while a musical theme incorporating the Flute jingle from the original LoZ played was just...awesome. Kinda set the ambience for what was (to me, at least) a lonely, but happy, nostalgic, but melancholy almost coming of age journey.
Final Fantasy VII intro. Stars in space fading into mako, close up on Aerith's face, zoom out over the whole of Midgar, fast cuts to a speeding train, ending with Cloud (and the player) beginning their journey. Super cool way to introduce a setting, set up scale, and show that characters from all over this big city will eventually be related to each other.
And the single shot ending of Ground Zeroes, just for how cool and cinematic it was. I don't have much to say about it, I just think it's neat.