FF4 for RPGs... I did think Dragon Warrior was cool but I didn't own it and found it confusing as a young kid. Couple years later though, I tried FF2(4) on SNES though, and it was a game changer. 'Woah... this has a story, it's really interesting... and wow leveling is cool it feels like I'm building toward something or gaining something.' After that, Elder Scrolls Daggerfall and Shadowrun (Sega Genesis), then... Anarchy Online/Dark Age of Camelot (summer 2001) basically sealed the deal for open world RPGs and non-linear RPG exploration/leveling.
Strategy I guess was first Romance of the Three Kingdoms 2 (SNES) but it was really Warcraft 2, Ogre Battle, and Knights & Merchants that first got me into strategy via real time tactics/base building, then XCOM and Syndicate Wars adding a more management/tactics to my interests, Tactics Ogre and FFT for tactics RPGs, and finally Romance of the Three Kingdoms 4 on PSX that got me into grand strategy. Coincidentally, those 4-5 years or so as a teenager are why I ended up in economics TBH.
Then... I guess Metal Gear Solid and Tenchu for action or third-person. I was never a big action, adventure, or platformer fan. I mean, I loved and fully completed Super Mario World on SNES because who didn't, and Yoshi's Island... and there was one Contra on Sega Genesis that was bad ass. but in general I don't really like platformers, run and gun shooters, or most action or adventure games in general. Then MGS and Tenchu came along with the 3D action infiltration and everything changed for me.
Lastly, I guess it was Unreal Tournament and Medal of Honor AA that made me fall in love with MP and SP FPS, respectively. They were coincidentally my first real FPS games in general on my first 'good' PC with top graphics, surround sound, and high frame rate haha -- what a game changer that was. First time I played UT at max frame rate with surround sound was as big of a deal to me as playing my first RPG or playing Super Mario 64 for the first time. It was like, holy shit, this action let me catch me breath.
Those first 3 though are basically why my main 'regular' sort of trinity of gaming is basically MGS V and GTA V, supported by games like Tropico 5 and XCOM, and FF XII or Witcher 3. And then dabble in some FPS basically because I need a couple months of something that reminds of Unreal Tournament, MOHAA, or Enemy Territories: Wolfenstein.