I'm going to go on record as having said Final Fantasy VI is my favorite 16bit RPG, already.
But since that's been mentioned several times in this thread I thought I'd offer a close runner up; Terranigma. If you do not live in Japan or PAL regions this will be a hard game to get a hold of because it was not released in the US. And I simply cannot understand why! It is a masterpiece. It is the third of a line of games that are "spiritually" related, if not direct sequels; the other two being the primitive Soul Caliber, and the prequel to Terranigma called Illusion of Gaia.
There are fan made translation patches you can find with a google search which are easily applied to roms of the game, and that is a fine way to play it. But it's just a shame the title has never made its western debut, especially in the age of omnipresent virtual consoles.
I wont give away too many details for those of you who may be interested in playing the game, but it features a boy who does a bad thing which dooms him to wander through time, essentially acting as a safe guard for the progression of the Earth through various epochs. The characters are all wonderful, the story is that uniquely Japanese blend of touching and comical that only they do right, and the graphics are well above average for a Super Nintendo title.
If you're an RPG fan you do yourself a disservice by not looking this one up. It's an instant classic.