sorry, just something about Final Fantasy : a lot of people would recommend their first Final fantasy.
people who played all/most of them would recommend FF4 and FF6. (I never played FF4, but I can recommend 6).
there are so many JRPG, it's hard to just recommend some.
The "Tales of" series is well acclaimed. I'd recommend the first one on Snes (tales of Phantasia), that's the only one I played so I'll let other users suggest more. I tried the beginning of tales of "destiny", "symphonia", "the abyss". I liked a lot destiny.
The star ocean series is also similar to Tales of. same concept/menu/battle system.
Super Mario RPG, even if it looks different, it's a JRPG.
Snes had a lot of JRPG. like Breath of fire, Dragon quest (though, not all translated to english), Lufia to name the more suggested and well known.
One of my preferred JRPG is Xenogears (on PS1, you can play the game with a Wii and WiiSXR).
Xenoblade on Wii, it's mixed with people who liked it and ones who didn't like the battle system.
On DS, I liked a lot Glory of Heracles. it's a little linear, but story and battle system are great.
on DS/3DS, I'd recommend Radiant Historia. (non linear parallel and time travel)
I don't know, too much to remember/list. that's the only one coming to mind right now.
You only want JRPG? not tactical ? not ARPG? or maybe you don't know this genre and you might like it. but again, there are so many different sub-genre, it's hard to suggest without knowing your tastes.
edit: too bad you didn't mention PS2/PS3/PS4, there are Persona series you could try (persona 4 is often suggested). PS1/PS2 have a lot of JRPG too. PS1 can be emulated on Wii.