Can't believe there are those still willing to play these classics (oh god, I have a whole list, so bear with me).
Suikoden II - clean and well made RPG but is a classic so it is harder to find
Ogre Battle - another classic that would be hard to find but is a very good strategy/RPG that sets apart from the others
Azure Dreams - Lots of stuff to do in this RPG and if bad graphics aren't a problem then I would recommend this
Legend of Dragoon - The first one on my list that is a 3D RPG. Personally I loved this one, and even my friends who hate RPGs liked it.
Vandal Hearts - another strategy/RPG like FF Tactics and Ogre Battle. Highly reccomended.
If you can, get all the FF's even some are not that great because they're great to have. Plus, I think FF6 is multi-player.
All the rest are recommended but I have no personal experience with these games:
Beyond the Beyond
Legend of Legaia
Alundra (not the second one)
Tales of Destiny
Grandia (I've played it a little but I stopped playing because of the story line)
Guardian's Crusade (better for starting RPGers)
Well, Have fun!