First off, my list. I no particular order:
Shadow Hearts series (Koudelka, Shadow Hearts 1-2 are all one continuous story. From the New World wasn't all that good)
The World Ends With You (Great soundtrack, uplifting message that isn't corny)
Arcanum (Lots of depth... when it decides to work)
Final Fantasy 12 (Love the story in this)
Vagrant Story (Love the story in this even more than 12)
Final Fantasy Tactics (Once again, great story. All of the Ivalice Alliance titles do)
Wild Arms 3 (Awesome soundtrack)
Persona 4 (Less depressing than 3, with more control of your allies)
Pokemon series (Surprising amount of depth, considering the hardware and graphic limitations)
Ok, now to some comments.
For one, all the special moves that the game teaches you early on (Gau's animal mimicry, Sabin's moves, etc) are pretty much left aside in favour of magic by the second half of the game. The spells were, of course, much more powerful, so it was always a matter of training everyone on everything. You compare that with my #1 fave game, FF IV. Each of the characters' abilities were used right to the very end.
Gau's actually more powerful without magic than he is with it., thanks to some game breaking combos he can do. For instance, his Stray Cat lure has an attack that does 8x his normal attack damage to one target, making him absurdly powerful. Combine this with a Merit Award (Gau can now use any weapon or armor), a Tempest (Sword for Cyan that does Wind Damage and occasionally hits all enemies for wind damage), and maybe a Genji Glove/Offering + another Tempest... what you get is someone who can hit enemies very hard, very often with an element few resist and who can hit ALL OF THEM for the same amount of damage fairly often. For free. Plus you can put a Snow Muffler on him thanks to the Merit Award, giving him great defenses.
Sabin still sucks later on though.
Two, I've always felt that, after Kefka destroys the world, the pace of the story grinds to a halt. Before, it was "Go here, then here, then here, then here" as you world trotted and the story never stopped. But then, after the world ends, the game becomes "collect all your crew, grind, beat Kefka". I felt FF VII kinda did this, too, after Meteor was summoned.
I think that was intentional in FF6. Kefka had already won... he controlled the world and had put terror into the hearts of even some of your own companions. At that point, what else can you do? You just look for your friends, ask them what they want to do, and the make sure your powerful enough to succeed. It makes sense, even if it's sort of depressing.
As for FF7... once Meteor shows up, the cast know there really isn't too much they can do to stop it. At that point, it's about resolving personal storylines (Barret, Cloud, Tifa, Vincent, Cait Sith, and Cid). Once they've done all of that, it finally dawns on them that maybe Aerith knew what she was doing after all. I'll admit that it's slow, but that stuff was necessary for plot reasons.