Hmm....best game? Hard one really.
Though I would say the following, as I honestly can't name just 1 or 2:
Storywise: really think Xenogears for the Playstation was extremely good and a fun game to boot.
RPG-wise: likely Final Fantasy 3 (as thats what I knew it as, but otherwise Final Fantasy VI) and Chrono Trigger likely. Closely followed by Suikoden 2.
Fighting games: Street Fighter 2 Alpha 3 is perhaps my favorite of that genre.
Other: Excitebike on the NES, Legend of Zelda: Link to the Past on SNES, Lunar Silver Star Story Complete for Playstation.
Really could likely name many others, just these are the ones I think of first.