Final Fantasy 7 was the reason I bought the console and started paying attention to gaming again. I still remember when I saw the commercial for the first time, it blew me away. My friend was talking to me and I completely shut them out until the commercial was over. I had an SNES before that but playing games on it rarely felt immersive or meaningful--until I found Final Fantasy 6 in a used game store that my friend dragged me into. I'd played Final Fantasy (1) on the NES and didn't even know that there were more of them. FF6 instantly became my favorite game by a mile but I couldn't find anything else like it and kind of dropped out of gaming as a hobby. At least, until that FF7 commercial hit me like a bomb.
Honorable mentions to Gran Turismo, Suikoden, and Soul Blade, all of which were absolutely awesome experiences that still live in my memory.