I'll third or whatever Golden Axe. People complain about the conversion, but the arcade didn't have that fun pit stage.
I play a lot of JRPGs, just as a warning here -
Phantasy Star II: Crisp futuristic graphics and a grim, mature story told in a unique sideways way. Plus, had that particularly heartbreaking story twist way before FF7.
Phantasy Star IV: It's an CD anime game in cart form, if that makes any sense. I question its current popularity and hype as the "only tolerable 16-bit RPG", though; it's way too easy, with brain-dead dungeons, for one.
the Lunar series: Color, charm, and my favorite RPG villain and character, with CD sound and song playing a big part in the stories. (Sega CD Eternal Blue is actually better than the Saturn/PS remake due to some weird art and story choices in the latter's cutscenes.)
Popful Mail: Working Designs was known for putting immature humor in inappropriate places, but Popful Mail was a happy parody of RPG adventure, so the humor fit right in. It also featured metric tons of stellar, hilarious voice acting throughout; probably Working Designs' best writing effort.
Final Fantasy II: It was my introduction to character-driven RPGs, and it still has big charm today.
Chrono Trigger: Well, duh. I don't think it's the god game everyone else does, but it's pretty darn close.
Secret of Mana: The story is incoherent, but the music is lovely, and the romp-through-nature beat-em-up gameplay is both beautiful and satisfying.
Lufia and the Fortress of Doom: The gameplay is rather unremarkable, but the dialogue is fresh and natural, particularly for the day, and the love story is one of the best in any RPG. That ending - what a heartrender. (I'm not much for the sequel; I found the characters largely grating and the love story cardboard and unbelievable, though I know my opinion is in the minority.)
Clock Tower: Hey, a non-RPG! An endlessly clever 16-bit interpretation of the horror genre that achieves a heck of a lot in its small format and is truly, memorably scary.
