I mean, Crono didn't even speak. Not once. But, when [spoiler] he "died"... I don't know, I still get a bit choked up at Marle breaking down in front of the tree. Same for Lufia II when Maxim and Selan [spoiler] die at the end. I felt like I was losing a friend. I just haven't found emotion like that in modern games.
For me it was all about story. I love great gameplay, but I wanted to be engrossed in a storyline while I played the game. That's why I played RPG's to begin with.
I have found games since the 16-bit era which have had the same effect (FF IX, FF Tactics, Kingdom Hearts I & II, and Suikoden I & II to name a few), but there seemed to be an abundance of them on the SNES. Modern RPG's just don't feel the same to me. I still play my SNES favorites every year when I can find the time.
I'm going out on a bit of a limb here, but I wonder if the limitations of the hardware didn't force the creators to be more creative in different areas. I mean, there was only so much you could do on the SNES (even though they managed to do some cool things on such a limited platform.)
After it was all said and done, the games had to offer more than cool looking pixels. The great games had great stories, interesting characters, and innovative gameplay (to be fair, it was probably easier to be innovative in those days.) Graphics were less of a concern.