My very first RPG was Earthbound, which I'd now state as my favorite game, so it was very natural to fall in love with RPGs after that.
As far as Simulation games go, my cousin gave me a copy of SimCity for Win 3.1. Sim games became a love for me. And then I found Harvest Moon...
I played some RTSes back with Civilization II and Alpha Centari, but I really got into them with Age of Empires II, running a CAT 5 down the hallway to my sister's room. Adding a live opponent made all the difference.
And Action RPGs, Ocarina of Time, easily. I actually never played a Zelda game until that one, and just fell in love with everything about it.