Front Mission, Vagrant Story, Chrono Cross, the Mana series, Saga series, Parasite Eve, etc.
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To expand on what Del is referring to, Secret of Mana was the first game to really utilize the Mode 7 effect to create a pseudo 3D world map, a program later used in FFVI for great effect. Hell, technically the open ended nature of VI and CT was accidentally created in Mana as it's possible to do most of the last third of the game in any order as long as you know where to go without pushing the story mode making the whole scene with Sage Joch pretty amusing...
The SaGa franchise would also utilize gameplay mechanics that eventually found their way into the FF titles and vice versa. Games like Brave Fencer Musashi used boss battles where you're running from an enemy that got incorporated into VIII's running from the Spider Mech as well as Squaesoft's first foray into Voice acting. The interactive gunblade mechanic from VIII got it's origins from Square's work on Mario RPG. Chrono Cross' battle system is a variation of Xenogears system, several monster and architectural designs in XII are almost lifted verbatim from Vagrant Story. The Bouncer served as a trial run for the visual design for FFX and FFVII's use of different gameplay and minigames to freshen and involve the player more into the game traces itself back to Chrono Trigger which itself traces back to FFVI. You could see a lot of cross-pollination in the old days which ended after the merger.