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Etrian Odyssey
Etrian Odyssey II: Heroes of Lagaard
Etrian Odyssey III: The Drowned City
Final Fantasy: The 4 Heroes of Light
Infinite Space
Radiant Historia
Shin Megami Tensei: Devil Survivor
Shin Megami Tensei: Devil Survivor 2
Shin Megami Tensei: Strange Journey

Dragon Quest IV: The Chapters of the Chosen
Dragon Quest V: The Hand of the Heavenly Bride
Dragon Quest VI: Realms of Reverie
Dragon Quest IX: Sentinels of the Starry Skies
Inazuma Eleven
Inazuma Eleven 2: Blizzard
Mystery Dungeon: Shiren the Wanderer
Suikoden Tierkreis
The World Ends with You
Valkyrie Profile: Covenant of the Plume

Contact
Dragon Quest Monsters: Joker
Final Fantasy IV
Rhapsody: A Musical Adventure
Solatorobo: Red the Hunter
The Dark Spire

Final Fantasy III
Even though they're not ranked at the top I strongly recommend Infinite Space and Inazuma Eleven for originality. The story in the Inazuma games is made for kids and boring as hell, but the stylus controlled action parts of the game are excellent.
Edit: You know what. Feel free to dock a point from Etrian 2, 3, Devil Survivor 2, and Strange Journey since they're cheap rehashes.