I'll just speak from experience:


JRPGs - Final Fantasy VII. It was the gateway to both Japanese and role-playing games for me. Never looked back since.

Fighting games - Street Fighter II & Super Smash Bros. 64. I actually started with SFII Turbo on SNES, but I really got into them with SSB64.

2D Platformers - Donkey Kong Country. It was my first ever platformer, and it's still one of my favorites to this day. Got me into other games including Super Mario World.

3D Platformers - Super Mario 64 & Banjo Kazooie. SM64 is considered the best game of all time by many for a good reason. :P