FFVII in pc sure is bad port but the game is the same.
Star ocean 2 was hell of a game.
I did play grandia 1 but not 2.

I feel like I'm the only one who knows this game:

Treasure of the Rudras for the SNES

http://www.fantasyanime.com/valhalla/rudra.htm

I was very big into JRPGs in the SNES era before switching to Western RPGs with Baldur's Gate and Fallout. I played some JRPGs into the PS1 and PS2 eras but not with the same affection at all, and only the hugely popular ones.

Anyway my favorites would be Final Fantasy VI, Chrono Trigger and Secret of Mana. I would guess all of those are good for getting into the genre if you can deal with SNES graphics. If you need something more modern I hear Lost Odyssey on the Xbox is very good, though I wouldn't know.

In jrpg games, those graphics are still pretty good IMO.

The YS games have PC ports. Worth checking out.

Was going to suggest the recent Shin Megami Tensei titles, but those are console-only. Shame.

There is a silly indie JRPG or two on Steam, Recettear, Chantelise, and the parody/homage Crhulhu Saves the World.

Another good parody that is actually free is Charles Barkley Shut up and Jam Gaiden. It is actually GREAT.

I know I'm a minority, but I liked The Last Remnant. Pretty good game IMHO, not amazing, but I got over 50 hours of gameplay for it, so I feel it was worth it even when I never finished it.

Also, Generica. Early JRPG "clone". Does the generic stuff of the 80's including palette swap monsters, but does it damn well.
Also, Iffermoon http://www.rpgfan.com/reviews/Iffermoon/index.html Add The Desolate Room and Flan Rising by the same developer. Very well put together.
Ah, Hero;s Realm http://rpgmaker.net/games/82/
The Spirit Engine are well-drawn but the combat tends to drag for some reason. TSE2 was payware, but lack of sales encouraged the developer to release it for free.

Exceptions made for GBA versions.

The Sega CD versions still hold up as good RPG's, the PSX version did change some significant story details, so I recommend playing the originals.

I can't recommend any new JRPG's since I really stick to the older games, but here are some:

Dragon Quest/Warrior IV
Final Fantasy IV (II US)
Final Fantasy VII
Chrono Trigger

I meant the PSX and not this wannabee Gameboy clone

I've started playing Septerra. It has struck me as being a cross between FF and Fallout but I'm not very far in. The interface and magic is different and looks interesting and the story has intrigued me, not bad so far for £3. Don't anyone post spoilers!!
Agreed. I actually don't mind the old-school graphics. Since most old Japanese game animation is based on manga/anime it has aged really well, especially when compared to Western RPGs.

Those 3 are among my favorites on the SNES too, I may add that the sequel to Secret of Mana, Seiken Densetsu 3, was even better than the original but it was only released on Japan. Fortunately, there is a fan translation for it.
Other great JRPGs for the SNES were: Super Mario RPG (it was made by Square in collaboration with Nintendo) and Tales of Phantasia.

Lol. I think I will need to make a to-do-list.

Septerra combat is straight from Final Fantasy 7, except they forgot the part about making all the ambient animations fun to watch. It would have worked much better using FFX's method of jumping straight to the next available action window. Good game despite that, great story.

Septerra, Grandia 2, Final Fantasy 7 and 8, Last Remnant, Breath of Death + Cthulhu, those are probably the best you'll find in PC retail for that style of game. There are some other FF style games floating around, like Aveyond and the Laxius series.

Every so often something gets ported from Japan, but those are hard to keep track of. You could try a Mobygames search.
http://www.mobygames.com/browse/games/anime-manga/dos/role-playing-rpg
http://www.mobygames.com/browse/games/role-playing-rpg/windows/top-down/anime-manga

If you like first-person gameplay with an emphasis on combat, and don't mind dated graphics and interface, you might enjoy the Wizardry and Might & Magic series. Wizardry even had a few Japanese spinoffs with anime graphics.

There are also a number of Sega Genesis ports legally available for Windows. You might be able to find some of the Phantasy Star games among them.

As someone who has never really enjoyed JRPGs for their story and setting I'll have to recommend Chrono Trigger as well. Its one of the very few I've ever held an instrest in and completed. The fact they were all little kids didn't bother me in this game either.