Ocarina of Time. It was just the perfect game. I spent weeks arguing with a classmate in art class that Turok 2 was better. He loaned me OoT. I didn't even like games unless they were Mortal Kombat or bloody shooters. OoT just blew my 12 year old mind.
Super Mario 64 helped a lot as well. It was a cut above everything on PS1 by a huge margin. PS1 games felt like they were living in the past with a lot of 2D games, or games that didn't use an analogue stick. SM64 and OoT just moved the industry forward so damned much. Nintendo continues that today with BotW, and Odyssey.