I really like Romancing SaGa: Minstrel Song.
The world may be in separate pieces, but the game is non-linear, with most of it consisting of exploring the various towns, talking to people, and discovering some sidequests to do, then doing this. Also, events happen as time passes (which is defined by the number and difficulty of the battles you fight), which can result in quests opening and closing, as well as events such as cities being attacked. The game also has a very unconventional growth system, as well, where actions determine stat growth and occasionally, you'll glimmer a new ability when attacking (a light bulb appears over the character's head, and the character will immediately use a newly learned attack). One thing I find interesting is how this game straddles the line between JRPG and WRPG. (Worth noting that I enjoyed this game more than Dragon Quest 8.)
I could also mention Metal Saga (no relation to the SaGa series), which is basically a post-apocalyptic JRPG with the artificial barriers to exploration removed. The game is a bit rough around the edges, however, but you at least get to drive around in tanks and fight enemies while doing so.
Edit: Also, for the PlayStation 1:
* SaGa Frontier, for many of the playable characters, is open world from the start, though again the world is segmented into different regions. (One warning: Don't play Lute's quest first. It may be the most open of all of them, but that unfortunately means you can get trapped in the final dungeon before you're strong enough to beat the game (and before you understand the game's basic systems). I recommend Blue if you want an open-world experience that requires you to do things before the endgame.) (Also, Asellus is queer.)
* Final Fantasy 2 (from Final Fantasy Origins) is open world in the sense that you can go almost anywhere at the start, provided you are strong enough (and you won't be at the start). However, the game is still linear, in that there's usually only one dungeon to explore at any given point, and the world is rather empty. Also, the PSX version is unfortunately one of the worst versions of the game, as spells level up more slowly than in even the original Famicom version.
* Also, in Japan there's a PSX port of Wizardry 7, which would technically qualify here. Since it's only available in Japanese, you might prefer to play the English DOS version instead (which you can get in the extras of GOG's Wizardry 6+7 pack). (Wizardry 8 is also open world once you get past the start, but that game has no console port, so it technically doesn't qualify for purposes of this topic.)
Edit 2: Note that SaGa Frontier 2 is *not* open world; it is a good game, but it's very different from SaGa Frontier 1.
Post edited January 10, 2021 by dtgreene