Designed by: Several people
Influenced by: Final Fantasy, Falcom RPGs
Series: Not a coherent series, this is a catch-all category for a group of games that share some attributes.
Legacy: Later Final Fantasy games, probably.
Back in Square's design heyday, before the era of Final Fantasy VII and long before they merged with long-time rival Enix, they produced a number of highly unique Super Famicom games that did some very interesting improvisation around the theme of role-playing. Many of them are a bit obscure today, overshadowed by the Final Fantasy series, but there are some very interesting ideas to be found there.
In a way, they're kind of like counterparts to the Falcom RPGs; they're a lot more traditional, but they show some of the same ingenuity in design. When people obsess about JRPGs, there's a good chance that some of these games are part of the reason why.
Also like the Falcom RPGs, few of these games made it to the U.S during the 16-bit era. Some of them are:
This is probably the best-known of the lot today, and rightfully considered one of the best of all JRPGs. It's probably the best RPG ever made with a time travel theme. It's particularly beloved now for its charming characters and influential "New Game +" mode, allowing players to start over once the game is finished with the levels, stats and most of the equipment from the previous playthrough.
A lot has been made of the many endings available in New Game +; I actually think most of these are overrated; they're novel but not really relevant to the game's narrative. Many of them are played for laughs.
However, one thing about the game that is unquestionably awesome is the main villain, Lavos, an alien, Lovecraftian entity who never speaks or gloats, and who receives perhaps the most impressive buildup of any big baddie in an JRPG.
Seiken Densetsu (series), a.k.a. "the Mana games":
The second and third games of this series are the ones that fall into this period of Square's history, and are probably the best. Seiken Densetsu 2 made it to the U.S. as Secret of Mana; given how many fans it had, Seiken Densetsu 3 is still infamous for its lack of a localized release. They have generally excellent multiplayer play, especially part 2, which supported up to three people playing at once, and excellent graphics and character art.
Romancing SaGa (series):
A subset of the larger SaGa series. These games tend to stray more towards the open-endedness of Western RPGs than JRPGs. Despite this, the character graphics have a strong 16-bit Final Fantasy vibe.
A tactical strategy game with Final Fantasy-like combat scenes and other cool concepts. Many of your characters have dragons who follow them into battle, and can be controlled individually. Most interesting is the enemy battle art, which at first glance looks like static art along the lines of 16-bit Final Fantasy monsters, until one of them attacks and it turns out they're actually made out of segmented sprites, like in Vanillaware's Odin Sphere -- and animated!
Live a Live:
A unique game in which the player completes different scenarios in different time periods. The scenarios are largely unconnected at first, but later on revealed to be connected (of course.) Many of the scenarios play quite differently from the others, giving this game a lot of variety.
Treasure of the Rudras:
Contains one of the most interesting magic systems ever seen in an RPG, J or otherwise. The player enters a name for each of his party's spells -- any name -- and the game determines the spell's attributes from it. It's not use a case of using a hash of the name's text either; there are hints given in the game for ways to make more powerful spells.
It's quite amazing, and worthy of study. There is an unofficial fan translation of this game, a great feat considering that, since the original spell system was heavily tied to Japanese, it basically had to be reimplemented.