I am tempted to say Chrono Trigger, even though, looking back at it objectively, it's not that great a game. Still, I love it because for me, characters make everything, and this was the first game I ever played where I could choose the characters in the party and they all had dialogue that clearly belonged to them.
I think my real choice is Megaman X3, though. That game is hard as hell but not infuriatingly so (looking at you, Megaman X5-7, and for the first time in a Megaman game, it has multiple paths so the choices you make early in the game will affect the layout of maps and even the bosses you face and weapons you gain.
Honorable mention goes out to Yoshi's Island, which has amazing graphics and some of the best, most interesting and inventive platform challenges you're ever going to see in a 16-bit game. Plus, I love how much it embraces the absolute acid-trip weirdness of the Mario franchise: Touch a bubble and it turns a boot-wearing dinosaur into a helicopter because why wouldn't it?