Playstation 1:
Grandia (awful voice acting, great everything else)
Chrono Cross
Legend of Dragoon
Star Ocean: The Second Story
Jade Cocoon (kind of like Pokemon, but with a deep mythology behind it)
Super Nintendo:
Lufia 2 (it's a prequel, so you can safely skip the atrociously-dated first one)
Chrono Trigger
Earthbound
Breath of Fire (kind of generic, but still fun)
Breath of Fire 2 (full of missing punctuation, but still a great game)
iOS:
The Chaos Rings games. Especially 2, which is easily one of my favorite jRPGs to date, and a game that far too few people have heard of.
Lets see, let's see... Radiant Historia for the DS is great, as is Grandia 2 for the Dreamcast or PC or PS2. Tales of Phantasia, too... which I think is for the Game Boy Advance and maybe the PSP, can't remember. Also, if Japanese action-RPGs count as jRPGs, be sure to look into a fan-translated ROM of the brilliant Japan-only Seiken Densetsu 3.